{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Temporal Matrix Factorization\n",
    "\n",
    "**Published**: October 8, 2019\n",
    "\n",
    "**Author**: Xinyu Chen [[**GitHub homepage**](https://github.com/xinychen)]\n",
    "\n",
    "**Download**: This Jupyter notebook is at our GitHub repository. If you want to evaluate the code, please download the notebook from the repository of [**tensor-learning**](https://github.com/xinychen/tensor-learning/blob/master/content/BTMF.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Abstract\n",
    "\n",
    "Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this work, we propose a Bayesian Temporal Matrix Factorization (BTMF) model for modeling multidimensional time series - and in particular spatiotemporal data - in the presence of missing data. By integrating low-rank matrix factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, our model can effectively perform predictions without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and test the proposed BTMF on several real-world spatiotemporal data sets for both missing data imputation and short-term rolling prediction tasks. This post is mainly about BTMF models and their **`Python`** implementation with an application of spatiotemporal data imputation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Motivation\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Problem Description\n",
    "\n",
    "We assume a spatiotemporal setting for multidimensional time series data throughout this work. In general, modern spatiotemporal data sets collected from sensor networks can be organized as matrix time series. For example, we can denote by matrix $Y\\in\\mathbb{R}^{N\\times T}$ a multivariate time series collected from $N$ locations/sensors on $T$ time stamps, with each row $$\\boldsymbol{y}_{i}=\\left(y_{i,1},y_{i,2},...,y_{i,t-1},y_{i,t},y_{i,t+1},...,y_{i,T}\\right)$$\n",
    "corresponding to the time series collected at location $i$.\n",
    "\n",
    "As mentioned, making accurate predictions on incomplete time series is very challenging, while missing data problem is almost inevitable in real-world applications. Figure 1 illustrates the prediction problem for incomplete time series data. Here we use $(i,t)\\in\\Omega$ to index the observed entries in matrix $Y$.\n",
    "\n",
    "<img src=\"../images/graphical_matrix_time_series.png\" alt=\"drawing\" width=\"500\"/>\n",
    "\n",
    "> **Figure 1**: Illustration of multivariate time series and the prediction problem in the presence of missing values (green: observed data; white: missing data; red: prediction).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Model Description\n",
    "\n",
    "Given a partially observed spatiotemporal matrix $Y\\in\\mathbb{R}^{N \\times T}$, one can factorize it into a spatial factor matrix $W\\in\\mathbb{R}^{R \\times N}$ and a temporal factor matrix $X\\in\\mathbb{R}^{R \\times T}$ following general matrix factorization model:\n",
    "\\begin{equation}\n",
    "Y\\approx W^{\\top}X,\n",
    "\\label{btmf_equation1}\n",
    "\\end{equation}\n",
    "and element-wise, we have\n",
    "\\begin{equation}\n",
    "y_{it}\\approx \\boldsymbol{w}_{i}^\\top\\boldsymbol{x}_{t}, \\quad \\forall (i,t),\n",
    "\\label{btmf_equation2}\n",
    "\\end{equation}\n",
    "where vectors $\\boldsymbol{w}_{i}$ and $\\boldsymbol{x}_{t}$ refer to the $i$-th column of $W$ and the $t$-th column of $X$, respectively.\n",
    "\n",
    "The standard matrix factorization model is a good approach to deal with the missing data problem; however, it cannot capture the dependencies among different columns in $X$, which are critical in modeling time series data. To better characterize the temporal dependencies and impose temporal smoothness, a novel AR regularizer is introduced on $X$ in TRMF (i.e., Temporal Regularizer Matrix Factorization proposed by [Yu et al., 2016](https://www.cs.utexas.edu/~rofuyu/papers/tr-mf-nips.pdf)):\n",
    "\\begin{equation} \\label{equ:VAR}\n",
    "\\begin{aligned}\n",
    "    \\boldsymbol{x}_{t+1}&=\\sum\\nolimits_{k=1}^{d}A_{k}\\boldsymbol{x}_{t+1-h_k}+\\boldsymbol{\\epsilon}_t, \\\\\n",
    "    &=A^\\top \\boldsymbol{v}_{t+1}+\\boldsymbol{\\epsilon}_{t}, \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where $\\mathcal{L}=\\left\\{h_1,\\ldots,h_k,\\ldots,h_d\\right\\}$ is a lag set ($d$ is the order of this AR model), each $A_k$ ($k\\in\\left\\{1,...,d\\right\\}$) is a $R\\times R$ coefficient matrix, and $\\boldsymbol{\\epsilon}_t$ is a zero mean Gaussian noise vector. For brevity, matrix $A\\in \\mathbb{R}^{(R d) \\times R}$ and vector $\\boldsymbol{v}_{t+1}\\in \\mathbb{R}^{(R d) \\times 1}$ are defined as\n",
    "\\begin{equation*}\n",
    "A=\\left[A_{1}, \\ldots, A_{d}\\right]^{\\top} ,\\quad \\boldsymbol{v}_{t+1}=\\left[\\begin{array}{c}{\\boldsymbol{x}_{t+1-h_1}} \\\\ {\\vdots} \\\\ {\\boldsymbol{x}_{t+1-h_d}}\\end{array}\\right] .\n",
    "\\end{equation*}\n",
    "\n",
    "<img src=\"../images/rolling_prediction.png\" alt=\"drawing\" width=\"400\"/>\n",
    "\n",
    "> **Figure 2**: A graphical illustration of the rolling prediction scheme using BTMF (with VAR process) (green: observed data; white: missing data; red: prediction).\n",
    "\n",
    "In [Yu et al., 2016](https://www.cs.utexas.edu/~rofuyu/papers/tr-mf-nips.pdf), to avoid overfitting and reduce the number of parameters, the coefficient matrix in TRMF is further assumed to be a diagonal $A_k=\\text{diag}(\\boldsymbol{\\theta}_{k})$. Therefore, they have\n",
    "\\begin{equation} \\label{equ:AR}\n",
    "\\boldsymbol{x}_{t+1}=\\boldsymbol{\\theta}_{1}\\circledast\\boldsymbol{x}_{t+1-h_1}+\\cdots+\\boldsymbol{\\theta}_{d}\\circledast\\boldsymbol{x}_{t+1-h_d}+\\boldsymbol{\\epsilon}_t,\n",
    "\\end{equation}\n",
    "where the symbol $\\circledast$ denotes the element-wise Hadamard product. However, unlike Equation (4), a vector autoregressive (VAR) model in Equation (3) is actually more powerful for capturing multivariate time series patterns. \n",
    "\n",
    "<img src=\"../images/rolling_prediction_strategy.png\" alt=\"drawing\" width=\"400\"/>\n",
    "\n",
    "> **Figure 3**: A graphical illustration of the rolling prediction scheme using BTMF (with AR process) (green: observed data; white: missing data; red: prediction).\n",
    "\n",
    "In the following, we first introduce a Bayesian temporal matrix factorization model with an autoregressive model given in Equation (4), and then discuss another model with a vector autoregressive (VAR) model shown in Equation (3).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Bayesian Sequential Matrix Factorization (BSMF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Bayesian Temporal Matrix Factorization with Vector Autoregressive Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 Model Specification\n",
    "\n",
    "Following the general Bayesian probabilistic matrix factorization models (e.g., BPMF proposed by [Salakhutdinov & Mnih, 2008](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf)), we assume that each observed entry in $Y$ follows a Gaussian distribution with precision $\\tau$:\n",
    "\\begin{equation}\n",
    "y_{i,t}\\sim\\mathcal{N}\\left(\\boldsymbol{w}_i^\\top\\boldsymbol{x}_t,\\tau^{-1}\\right),\\quad \\left(i,t\\right)\\in\\Omega.\n",
    "\\label{btmf_equation3}\n",
    "\\end{equation}\n",
    "\n",
    "On the spatial dimension, we use a simple Gaussian factor matrix without imposing any dependencies explicitly:\n",
    "\\begin{equation}\n",
    "\\boldsymbol{w}_i\\sim\\mathcal{N}\\left(\\boldsymbol{\\mu}_{w},\\Lambda_w^{-1}\\right),\n",
    "\\end{equation}\n",
    "and we place a conjugate Gaussian-Wishart prior on the mean vector and the precision matrix:\n",
    "\\begin{equation}\n",
    "\\boldsymbol{\\mu}_w | \\Lambda_w \\sim\\mathcal{N}\\left(\\boldsymbol{\\mu}_0,(\\beta_0\\Lambda_w)^{-1}\\right),\\Lambda_w\\sim\\mathcal{W}\\left(W_0,\\nu_0\\right),\n",
    "\\end{equation}\n",
    "where $\\boldsymbol{\\mu}_0\\in \\mathbb{R}^{R}$ is a mean vector, $\\mathcal{W}\\left(W_0,\\nu_0\\right)$ is a Wishart distribution with a $R\\times R$ scale matrix $W_0$ and $\\nu_0$ degrees of freedom.\n",
    "\n",
    "In modeling the temporal factor matrix $X$, we re-write the VAR process as:\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\boldsymbol{x}_{t}&\\sim\\begin{cases}\n",
    "\\mathcal{N}\\left(\\boldsymbol{0},I_R\\right),&\\text{if $t\\in\\left\\{1,2,...,h_d\\right\\}$}, \\\\\n",
    "\\mathcal{N}\\left(A^\\top \\boldsymbol{v}_{t},\\Sigma\\right),&\\text{otherwise},\\\\\n",
    "\\end{cases}\\\\\n",
    "\\end{aligned}\n",
    "\\label{btmf_equation5}\n",
    "\\end{equation}\n",
    "\n",
    "Since the mean vector is defined by VAR, we need to place the conjugate matrix normal inverse Wishart (MNIW) prior on the coefficient matrix $A$ and the covariance matrix $\\Sigma$ as follows,\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "A\\sim\\mathcal{MN}_{(Rd)\\times R}\\left(M_0,\\Psi_0,\\Sigma\\right),\\quad\n",
    "\\Sigma \\sim\\mathcal{IW}\\left(S_0,\\nu_0\\right), \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where the probability density function for the $Rd$-by-$R$ random matrix $A$ has the form:\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "&p\\left(A\\mid M_0,\\Psi_0,\\Sigma\\right) \\\\\n",
    "=&\\left(2\\pi\\right)^{-R^2d/2}\\left|\\Psi_0\\right|^{-R/2}\\left|\\Sigma\\right|^{-Rd/2} \\\\\n",
    "&\\times \\exp\\left(-\\frac{1}{2}\\text{tr}\\left[\\Sigma^{-1}\\left(A-M_0\\right)^{\\top}\\Psi_{0}^{-1}\\left(A-M_0\\right)\\right]\\right), \\\\\n",
    "\\end{aligned}\n",
    "\\label{mnpdf}\n",
    "\\end{equation}\n",
    "where $\\Psi_0\\in\\mathbb{R}^{(Rd)\\times (Rd)}$ and $\\Sigma\\in\\mathbb{R}^{R\\times R}$ are played as covariance matrices.\n",
    "\n",
    "For the only remaining parameter $\\tau$, we place a Gamma prior  $\\tau\\sim\\text{Gamma}\\left(\\alpha,\\beta\\right)$ where $\\alpha$ and $\\beta$ are the shape and rate parameters, respectively. \n",
    "\n",
    "The above specifies the full generative process of BTMF, and we could also see the Bayesian graphical model shown in Figure 4. Several parameters are introduced to define the prior distributions for hyperparameters, including $\\boldsymbol{\\mu}_{0}$, $W_0$, $\\nu_0$, $\\beta_0$, $\\alpha$, $\\beta$, $M_0$, $\\Psi_0$, and $S_0$. These parameters need to provided in advance when training the model. However, it should be noted that the specification of these parameters has little impact on the final results, as the training data will play a much more important role in defining the posteriors of the hyperparameters.\n",
    "\n",
    "<img src=\"../images/btmf_net.png\" alt=\"drawing\" width=\"450\"/>\n",
    "\n",
    "> **Figure 4**: An overview graphical model of BTMF (time lag set: $\\left\\{1,2,...,d\\right\\}$). The shaded nodes ($y_{i,t}$) are the observed data in $\\Omega$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Model Inference\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the complex structure of BTMF, it is intractable to write down the posterior distribution. Here we rely on the MCMC technique for Bayesian learning. In detail, we introduce a Gibbs sampling algorithm by deriving the full conditional distributions for all parameters and hyperparameters. Thanks to the use of conjugate priors in Figure 4, we can actually write down all the conditional distributions analytically. Below we summarize the Gibbs sampling procedure.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1) Sampling Factor Matrix $W$ and Its Hyperparameters\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> For programming convenience, we use $W\\in\\mathbb{R}^{N\\times R}$ to replace $W\\in\\mathbb{R}^{R\\times N}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv as inv\n",
    "from numpy.random import multivariate_normal as mvnrnd\n",
    "from scipy.stats import wishart\n",
    "\n",
    "def cov_mat(mat):\n",
    "    new_mat = mat - np.mean(mat, axis = 0)\n",
    "    return np.einsum('ti, tj -> ij', new_mat, new_mat)\n",
    "\n",
    "def sample_factor_w(sparse_mat, binary_mat, W, X, tau):\n",
    "    \"\"\"Sampling N-by-R factor matrix W and its hyperparameters (mu_w, Lambda_w).\"\"\"\n",
    "    dim1, rank = W.shape\n",
    "    beta0 = 1\n",
    "    W_bar = np.mean(W, axis = 0)\n",
    "    var_mu_hyper = (dim1 * W_bar) / (dim1 + beta0)\n",
    "    var_W_hyper = inv(np.eye(rank) + cov_mat(W) + dim1 * beta0 / (dim1 + beta0) * np.outer(W_bar, W_bar))\n",
    "    var_Lambda_hyper = wishart(df = dim1 + rank, scale = var_W_hyper, seed = None).rvs()\n",
    "    var_mu_hyper = mvnrnd(var_mu_hyper, inv((dim1 + beta0) * var_Lambda_hyper))\n",
    "    for i in range(dim1):\n",
    "        pos0 = np.where(sparse_mat[i, :] != 0)\n",
    "        Xt = X[pos0[0], :]\n",
    "        var_mu = tau * np.matmul(Xt.T, sparse_mat[i, pos0[0]]) + np.matmul(var_Lambda_hyper, var_mu_hyper)\n",
    "        inv_var_Lambda = inv(tau * np.matmul(Xt.T, Xt) + var_Lambda_hyper)\n",
    "        W[i, :] = mvnrnd(np.matmul(inv_var_Lambda, var_mu), inv_var_Lambda)\n",
    "    return W"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) Sampling VAR Coefficients $A$ and Its Hyperparameters\n",
    "\n",
    "**Foundations of VAR**\n",
    "\n",
    "Vector autoregression (VAR) is a multivariate extension of autoregression (AR). Formally, VAR for $R$-dimensional vectors $\\boldsymbol{x}_{t}$ can be written as follows,\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\boldsymbol{x}_{t}&=A_{1} \\boldsymbol{x}_{t-h_1}+\\cdots+A_{d} \\boldsymbol{x}_{t-h_d}+\\boldsymbol{\\epsilon}_{t}, \\\\\n",
    "&= A^\\top \\boldsymbol{v}_{t}+\\boldsymbol{\\epsilon}_{t},~t=h_d+1, \\ldots, T, \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where\n",
    "\\begin{equation}\n",
    "A=\\left[A_{1}, \\ldots, A_{d}\\right]^{\\top} \\in \\mathbb{R}^{(R d) \\times R},\\quad \\boldsymbol{v}_{t}=\\left[\\begin{array}{c}{\\boldsymbol{x}_{t-h_1}} \\\\ {\\vdots} \\\\ {\\boldsymbol{x}_{t-h_d}}\\end{array}\\right] \\in \\mathbb{R}^{(R d) \\times 1}.\n",
    "\\end{equation}\n",
    "\n",
    "In the following, if we define\n",
    "\\begin{equation}\n",
    "Z=\\left[\\begin{array}{c}{\\boldsymbol{x}_{h_d+1}^{\\top}} \\\\ {\\vdots} \\\\ {\\boldsymbol{x}_{T}^{\\top}}\\end{array}\\right] \\in \\mathbb{R}^{(T-h_d) \\times R},\\quad Q=\\left[\\begin{array}{c}{\\boldsymbol{v}_{h_d+1}^{\\top}} \\\\ {\\vdots} \\\\ {\\boldsymbol{v}_{T}^{\\top}}\\end{array}\\right] \\in \\mathbb{R}^{(T-h_d) \\times(R d)},\n",
    "\\end{equation}\n",
    "then, we could write the above mentioned VAR as\n",
    "\\begin{equation}\n",
    "\\underbrace{Z}_{(T-h_d)\\times R}\\approx \\underbrace{Q}_{(T-h_d)\\times (Rd)}\\times \\underbrace{A}_{(Rd)\\times R}.\n",
    "\\end{equation}\n",
    "\n",
    "> To include temporal factors $\\boldsymbol{x}_{t},t=1,...,h_d$, we also define $$Z_0=\\left[\\begin{array}{c}{\\boldsymbol{x}_{1}^{\\top}} \\\\ {\\vdots} \\\\ {\\boldsymbol{x}_{h_d}^{\\top}}\\end{array}\\right] \\in \\mathbb{R}^{h_d \\times R}.$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Build a Bayesian VAR on temporal factors $\\boldsymbol{x}_{t}$**\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\boldsymbol{x}_{t}&\\sim\\begin{cases}\\mathcal{N}\\left(A^\\top \\boldsymbol{v}_{t},\\Sigma\\right),~\\text{if $t\\in\\left\\{h_d+1,...,T\\right\\}$},\\\\{\\mathcal{N}\\left(\\boldsymbol{0},I_R\\right),~\\text{otherwise}}.\\end{cases}\\\\\n",
    "A&\\sim\\mathcal{MN}_{(Rd)\\times R}\\left(M_0,\\Psi_0,\\Sigma\\right), \\\\\n",
    "\\Sigma &\\sim\\mathcal{IW}\\left(S_0,\\nu_0\\right), \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "&\\mathcal{M N}_{(R d) \\times R}\\left(A | M_{0}, \\Psi_{0}, \\Sigma\\right)\\\\\n",
    "\\propto|&\\Sigma|^{-R d / 2} \\exp \\left(-\\frac{1}{2} \\operatorname{tr}\\left[\\Sigma^{-1}\\left(A-M_{0}\\right)^{\\top} \\Psi_{0}^{-1}\\left(A-M_{0}\\right)\\right]\\right), \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "and\n",
    "\\begin{equation}\n",
    "\\mathcal{I} \\mathcal{W}\\left(\\Sigma | S_{0}, \\nu_{0}\\right) \\propto|\\Sigma|^{-\\left(\\nu_{0}+R+1\\right) / 2} \\exp \\left(-\\frac{1}{2} \\operatorname{tr}\\left(\\Sigma^{-1}S_{0}\\right)\\right).\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Likelihood from temporal factors $\\boldsymbol{x}_{t}$**\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "&\\mathcal{L}\\left(X\\mid A,\\Sigma\\right) \\\\\n",
    "\\propto &\\prod_{t=1}^{h_d}p\\left(\\boldsymbol{x}_{t}\\mid \\Sigma\\right)\\times \\prod_{t=h_d+1}^{T}p\\left(\\boldsymbol{x}_{t}\\mid A,\\Sigma\\right) \\\\\n",
    "\\propto &\\left|\\Sigma\\right|^{-T/2}\\exp\\left\\{-\\frac{1}{2}\\sum_{t=h_d+1}^{T}\\left(\\boldsymbol{x}_{t}-A^\\top \\boldsymbol{v}_{t}\\right)^\\top\\Sigma^{-1}\\left(\\boldsymbol{x}_{t}-A^\\top \\boldsymbol{v}_{t}\\right)\\right\\} \\\\\n",
    "\\propto &\\left|\\Sigma\\right|^{-T/2}\\exp\\left\\{-\\frac{1}{2}\\text{tr}\\left[\\Sigma^{-1}\\left(Z_0^\\top Z_0+\\left(Z-QA\\right)^\\top \\left(Z-QA\\right)\\right)\\right]\\right\\}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Posterior distribution**\n",
    "\n",
    "Consider\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "&\\left(A-M_{0}\\right)^{\\top} \\Psi_{0}^{-1}\\left(A-M_{0}\\right)+S_0+Z_0^\\top Z_0+\\left(Z-QA\\right)^\\top \\left(Z-QA\\right) \\\\\n",
    "=&A^\\top\\left(\\Psi_0^{-1}+Q^\\top Q\\right)A-A^\\top\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right) \\\\\n",
    "&-\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right)^\\top A \\\\\n",
    "&+\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right)^\\top\\left(\\Psi_0^{-1}+Q^\\top Q\\right)\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right) \\\\\n",
    "&-\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right)^\\top\\left(\\Psi_0^{-1}+Q^\\top Q\\right)\\left(\\Psi_0^{-1}M_0+Q^\\top Z\\right) \\\\\n",
    "&+M_0^\\top\\Psi_0^{-1}M_0+S_0+Z_0^\\top Z_0+Z^\\top Z \\\\\n",
    "=&\\left(A-M^{*}\\right)^\\top\\left(\\Psi^{*}\\right)^{-1}\\left(A-M^{*}\\right)+S^{*}, \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "which is in the form of $\\mathcal{MN}\\left(\\cdot\\right)$ and $\\mathcal{IW}\\left(\\cdot\\right)$.\n",
    "\n",
    "The $Rd$-by-$R$ matrix $A$ has a matrix normal distribution, and $R$-by-$R$ covariance matrix $\\Sigma$ has an inverse Wishart distribution, that is,\n",
    "\\begin{equation}\n",
    "A \\sim \\mathcal{M N}_{(R d) \\times R}\\left(M^{*}, \\Psi^{*}, \\Sigma\\right), \\quad \\Sigma \\sim \\mathcal{I} \\mathcal{W}\\left(S^{*}, \\nu^{*}\\right),\n",
    "\\end{equation}\n",
    "with\n",
    "\\begin{equation}\n",
    "\\begin{cases}\n",
    "{\\Psi^{*}=\\left(\\Psi_{0}^{-1}+Q^{\\top} Q\\right)^{-1}}, \\\\ {M^{*}=\\Psi^{*}\\left(\\Psi_{0}^{-1} M_{0}+Q^{\\top} Z\\right)}, \\\\ {S^{*}=S_{0}+Z^\\top Z+M_0^\\top\\Psi_0^{-1}M_0-\\left(M^{*}\\right)^\\top\\left(\\Psi^{*}\\right)^{-1}M^{*}}, \\\\ \n",
    "{\\nu^{*}=\\nu_{0}+T-h_d}.\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import invwishart\n",
    "\n",
    "def mnrnd(M, U, V):\n",
    "    \"\"\"\n",
    "    Generate matrix normal distributed random matrix.\n",
    "    M is a m-by-n matrix, U is a m-by-m matrix, and V is a n-by-n matrix.\n",
    "    \"\"\"\n",
    "    dim1, dim2 = M.shape\n",
    "    X0 = np.random.rand(dim1, dim2)\n",
    "    P = np.linalg.cholesky(U)\n",
    "    Q = np.linalg.cholesky(V)\n",
    "    return M + np.matmul(np.matmul(P, X0), Q.T)\n",
    "\n",
    "def sample_var_coefficient(X, time_lags):\n",
    "    dim2, rank = X.shape\n",
    "    d = time_lags.shape[0]\n",
    "    Z_mat = X[np.max(time_lags) : dim2, :]\n",
    "    Q_mat = X[np.max(time_lags) - time_lags[0] : dim2 - time_lags[0], :]\n",
    "    for k in range(1, d):\n",
    "        Q_mat = np.append(Q_mat, X[np.max(time_lags) - time_lags[k] : dim2 - time_lags[k], :], axis = 1)\n",
    "    var_Psi = inv(np.eye(rank * d) + np.matmul(Q_mat.T, Q_mat))\n",
    "    var_M = np.matmul(var_Psi, np.matmul(Q_mat.T, Z_mat))\n",
    "    var_S = (np.eye(rank) + np.matmul(Z_mat.T, Z_mat) - np.matmul(np.matmul(var_M.T, inv(var_Psi)), var_M))\n",
    "    Sigma = invwishart(df = rank + dim2 - np.max(time_lags), scale = var_S, seed = None).rvs()\n",
    "    return mnrnd(var_M, var_Psi, Sigma), Sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3) Sampling Factor Matrix $X$\n",
    "\n",
    "**Posterior distribution**\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "y_{it}&\\sim\\mathcal{N}\\left(\\boldsymbol{w}_{i}^\\top\\boldsymbol{x}_{t},\\tau^{-1}\\right),~\\left(i,t\\right)\\in\\Omega, \\\\\n",
    "\\boldsymbol{x}_{t}&\\sim\\begin{cases}\\mathcal{N}\\left(\\sum_{k=1}^{d}A_{k} \\boldsymbol{x}_{t-h_k},\\Sigma\\right),~\\text{if $t\\in\\left\\{h_d+1,...,T\\right\\}$},\\\\{\\mathcal{N}\\left(\\boldsymbol{0},I\\right),~\\text{otherwise}}.\\end{cases}\\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "If $t\\in\\left\\{1,...,h_d\\right\\}$, parameters of the posterior distribution $\\mathcal{N}\\left(\\boldsymbol{x}_{t}\\mid \\boldsymbol{\\mu}_{t}^{*},\\Sigma_{t}^{*}\\right)$ are\n",
    "\\footnotesize{\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\Sigma_{t}^{*}&=\\left(\\sum_{k=1, h_{d}<t+h_{k} \\leq T}^{d} {A}_{k}^{\\top} \\Sigma^{-1} A_{k}+\\tau\\sum_{i:(i,t)\\in\\Omega}\\boldsymbol{w}_{i}\\boldsymbol{w}_{i}^\\top+I\\right)^{-1}, \\\\\n",
    "\\boldsymbol{\\mu}_{t}^{*}&=\\Sigma_{t}^{*}\\left(\\sum_{k=1, h_{d}<t+h_{k} \\leq T}^{d} A_{k}^{\\top} \\Sigma^{-1} \\boldsymbol{\\psi}_{t+h_{k}}+\\tau\\sum_{i:(i,t)\\in\\Omega}\\boldsymbol{w}_{i}y_{it}\\right). \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "If $t\\in\\left\\{h_d+1,...,T\\right\\}$, then parameters of the posterior distribution $\\mathcal{N}\\left(\\boldsymbol{x}_{t}\\mid \\boldsymbol{\\mu}_{t}^{*},\\Sigma_{t}^{*}\\right)$ are\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\Sigma_{t}^{*}&=\\left(\\sum_{k=1, h_{d}<t+h_{k} \\leq T}^{d} {A}_{k}^{\\top} \\Sigma^{-1} A_{k}+\\tau\\sum_{i:(i,t)\\in\\Omega}\\boldsymbol{w}_{i}\\boldsymbol{w}_{i}^\\top+\\Sigma^{-1}\\right)^{-1}, \\\\\n",
    "\\boldsymbol{\\mu}_{t}^{*}&=\\Sigma_{t}^{*}\\left(\\sum_{k=1, h_{d}<t+h_{k} \\leq T}^{d} A_{k}^{\\top} \\Sigma^{-1} \\boldsymbol{\\psi}_{t+h_{k}}+\\tau\\sum_{i:(i,t)\\in\\Omega}\\boldsymbol{w}_{i}y_{it}+\\Sigma^{-1}\\sum_{k=1}^{d}A_{k}\\boldsymbol{x}_{t-h_k}\\right), \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where\n",
    "$$\\boldsymbol{\\psi}_{t+h_k}=\\boldsymbol{x}_{t+h_k}-\\sum_{l=1,l\\neq k}^{d}A_{l}\\boldsymbol{x}_{t+h_k-h_l}.$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_factor_x(sparse_mat, binary_mat, time_lags, W, X, tau, A, Lambda_x):\n",
    "    dim2, rank = X.shape\n",
    "    d = time_lags.shape[0]\n",
    "    mat0 = np.matmul(Lambda_x, A.T)\n",
    "    mat1 = np.zeros((rank, rank, d))\n",
    "    mat2 = np.zeros((rank, rank))\n",
    "    for k in range(d):\n",
    "        Ak = A[k * rank : (k + 1) * rank, :]\n",
    "        mat1[:, :, k] = np.matmul(Ak, Lambda_x)\n",
    "        mat2 += np.matmul(mat1[:, :, k], Ak.T)\n",
    "    for t in range(dim2):\n",
    "        pos0 = np.where(sparse_mat[:, t] != 0)\n",
    "        Wt = W[pos0[0], :]\n",
    "        Nt = np.zeros(rank)\n",
    "        if t >= np.max(time_lags):\n",
    "            Qt = np.matmul(mat0, X[t - time_lags, :].reshape([rank * d]))\n",
    "            if t < dim2 - np.max(time_lags):\n",
    "                Mt = mat2.copy()\n",
    "                for k in range(d):\n",
    "                    A0 = A.copy()\n",
    "                    A0[k * rank : (k + 1) * rank, :] = 0\n",
    "                    var5 = (X[t + time_lags[k], :] \n",
    "                            - np.matmul(A0.T, X[t + time_lags[k] \n",
    "                                                - time_lags, :].reshape([rank * d])))\n",
    "                    Nt += np.matmul(mat1[:, :, k], var5)\n",
    "            elif t >= dim2 - np.max(time_lags) and t < dim2 - np.min(time_lags):\n",
    "                index = list(np.where(t + time_lags < dim2))[0]\n",
    "                Mt = np.zeros((rank, rank))\n",
    "                for k in index:\n",
    "                    Ak = A[k * rank : (k + 1) * rank, :]\n",
    "                    Mt += np.matmul(np.matmul(Ak, Lambda_x), Ak.T)\n",
    "                    A0 = A.copy()\n",
    "                    A0[k * rank : (k + 1) * rank, :] = 0\n",
    "                    var5 = (X[t + time_lags[k], :] \n",
    "                            - np.matmul(A0.T, X[t + time_lags[k] \n",
    "                                                - time_lags, :].reshape([rank * d])))\n",
    "                    Nt += np.matmul(np.matmul(Ak, Lambda_x), var5)\n",
    "            inv_var_Lambda = inv(tau * np.matmul(Wt.T, Wt) + Mt + Lambda_x)\n",
    "        elif t < np.max(time_lags):\n",
    "            Qt = np.zeros(rank)\n",
    "            index = list(np.where(t + time_lags >= np.max(time_lags)))[0]\n",
    "            Mt = np.zeros((rank, rank))\n",
    "            for k in index:\n",
    "                Ak = A[k * rank : (k + 1) * rank, :]\n",
    "                Mt += np.matmul(np.matmul(Ak, Lambda_x), Ak.T)\n",
    "                A0 = A.copy()\n",
    "                A0[k * rank : (k + 1) * rank, :] = 0\n",
    "                var5 = (X[t + time_lags[k], :] \n",
    "                        - np.matmul(A0.T, X[t + time_lags[k] \n",
    "                                            - time_lags, :].reshape([rank * d])))\n",
    "                Nt += np.matmul(np.matmul(Ak, Lambda_x), var5)\n",
    "            inv_var_Lambda = inv(tau * np.matmul(Wt.T, Wt) + Mt + np.eye(rank))\n",
    "        var_mu = tau * np.matmul(Wt.T, sparse_mat[pos0[0], t]) + Nt + Qt\n",
    "        X[t, :] = mvnrnd(np.matmul(inv_var_Lambda, var_mu), inv_var_Lambda)\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_factor_x(sparse_mat, binary_mat, time_lags, W, X, tau, A, Lambda_x):\n",
    "    dim2, rank = X.shape\n",
    "    d = time_lags.shape[0]\n",
    "    for t in range(dim2):\n",
    "        pos0 = np.where(sparse_mat[:, t] != 0)\n",
    "        Wt = W[pos0[0], :]\n",
    "        Mt = np.zeros((rank, rank))\n",
    "        Nt = np.zeros(rank)\n",
    "        if t >= np.max(time_lags):\n",
    "            Qt = np.matmul(Lambda_x, np.matmul(A.T, X[t - time_lags, :].reshape([rank * d])))\n",
    "        if t >= np.max(time_lags) and t < dim2 - np.max(time_lags):\n",
    "            index = list(range(0, d))\n",
    "        elif t >= dim2 - np.max(time_lags) and t < dim2 - np.min(time_lags):\n",
    "            index = list(np.where(t + time_lags < dim2))[0]\n",
    "        elif t < np.max(time_lags):\n",
    "            Qt = np.zeros(rank)\n",
    "            index = list(np.where(t + time_lags >= np.max(time_lags)))[0]\n",
    "        if t < dim2 - np.min(time_lags):\n",
    "            for k in index:\n",
    "                Ak = A[k * rank : (k + 1) * rank, :]\n",
    "                Mt += np.matmul(np.matmul(Ak, Lambda_x), Ak.T)\n",
    "                A0 = A.copy()\n",
    "                A0[k * rank : (k + 1) * rank, :] = 0\n",
    "                var5 = (X[t + time_lags[k], :] \n",
    "                        - np.matmul(A0.T, X[t + time_lags[k] - time_lags, :].reshape([rank * d])))\n",
    "                Nt += np.matmul(np.matmul(Ak, Lambda_x), var5)\n",
    "        var_mu = tau * np.matmul(Wt.T, sparse_mat[pos0[0], t]) + Nt + Qt\n",
    "        if t < np.max(time_lags):\n",
    "            inv_var_Lambda = inv(tau * np.matmul(Wt.T, Wt) + Mt + np.eye(rank))\n",
    "        else:\n",
    "            inv_var_Lambda = inv(tau * np.matmul(Wt.T, Wt) + Mt + Lambda_x)\n",
    "        X[t, :] = mvnrnd(np.matmul(inv_var_Lambda, var_mu), inv_var_Lambda)\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4) Sampling Precision $\\tau$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_precision_tau(sparse_mat, mat_hat, position):\n",
    "    var_alpha = 1e-6 + 0.5 * sparse_mat[position].shape[0]\n",
    "    var_beta = 1e-6 + 0.5 * np.sum((sparse_mat - mat_hat)[position] ** 2)\n",
    "    return np.random.gamma(var_alpha, 1 / var_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5) BTMF Implementation\n",
    "\n",
    "- **Gibbs sampling**\n",
    "\n",
    "    - Burn-in process\n",
    "    - Sampling process\n",
    "\n",
    "\n",
    "- **Imputation**\n",
    "\n",
    "\n",
    "- **Prediction**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BTMF(dense_mat, sparse_mat, init, rank, time_lags, burn_iter, gibbs_iter):\n",
    "    \"\"\"Bayesian Temporal Matrix Factorization, BTMF.\"\"\"\n",
    "    \n",
    "    W = init[\"W\"]\n",
    "    X = init[\"X\"]\n",
    "    dim1, dim2 = sparse_mat.shape\n",
    "    d = time_lags.shape[0]\n",
    "    pos = np.where((dense_mat != 0) & (sparse_mat == 0))\n",
    "    position = np.where(sparse_mat != 0)\n",
    "    binary_mat = np.zeros((dim1, dim2))\n",
    "    binary_mat[position] = 1\n",
    "    tau = 1\n",
    "    mat_hat_plus = np.zeros((dim1, dim2))\n",
    "    for it in range(burn_iter + gibbs_iter):\n",
    "        W = sample_factor_w(sparse_mat, binary_mat, W, X, tau)\n",
    "        A, Sigma = sample_var_coefficient(X, time_lags)\n",
    "        X = sample_factor_x(sparse_mat, binary_mat, time_lags, W, X, tau, A, inv(Sigma))\n",
    "        mat_hat = np.matmul(W, X.T)\n",
    "        tau = sample_precision_tau(sparse_mat, mat_hat, position)\n",
    "        rmse = np.sqrt(np.sum((dense_mat[pos] - mat_hat[pos]) ** 2) / dense_mat[pos].shape[0])\n",
    "        if (it + 1) % 1 == 0 and it < burn_iter:\n",
    "            print('Iteration: {}'.format(it + 1))\n",
    "            print('RMSE: {:.6}'.format(rmse))\n",
    "            print()\n",
    "        if it + 1 > burn_iter:\n",
    "            mat_hat_plus += mat_hat\n",
    "    mat_hat = mat_hat_plus / gibbs_iter\n",
    "    final_mape = np.sum(np.abs(dense_mat[pos] - mat_hat[pos]) / dense_mat[pos]) / dense_mat[pos].shape[0]\n",
    "    final_rmse = np.sqrt(np.sum((dense_mat[pos] - mat_hat[pos]) ** 2) / dense_mat[pos].shape[0])\n",
    "    print('Imputation MAPE: {:.6}'.format(final_mape))\n",
    "    print('Imputation RMSE: {:.6}'.format(final_rmse))\n",
    "    print()\n",
    "    return mat_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 Spatiotemporal Missing Data Imputation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "\n",
    "tensor = scipy.io.loadmat('../datasets/Guangzhou-data-set/tensor.mat')\n",
    "tensor = tensor['tensor']\n",
    "random_matrix = scipy.io.loadmat('../datasets/Guangzhou-data-set/random_matrix.mat')\n",
    "random_matrix = random_matrix['random_matrix']\n",
    "random_tensor = scipy.io.loadmat('../datasets/Guangzhou-data-set/random_tensor.mat')\n",
    "random_tensor = random_tensor['random_tensor']\n",
    "\n",
    "dense_mat = tensor.reshape([tensor.shape[0], tensor.shape[1] * tensor.shape[2]])\n",
    "missing_rate = 0.4\n",
    "\n",
    "# =============================================================================\n",
    "### Random missing (RM) scenario\n",
    "### Set the RM scenario by:\n",
    "binary_mat = (np.round(random_tensor + 0.5 - missing_rate)\n",
    "              .reshape([random_tensor.shape[0], random_tensor.shape[1] * random_tensor.shape[2]]))\n",
    "# =============================================================================\n",
    "\n",
    "# binary_tensor = np.zeros(tensor.shape)\n",
    "# for i1 in range(tensor.shape[0]):\n",
    "#     for i2 in range(tensor.shape[1]):\n",
    "#         binary_tensor[i1, i2, :] = np.round(random_matrix[i1, i2] + 0.5 - missing_rate)\n",
    "# binary_mat = binary_tensor.reshape([binary_tensor.shape[0], binary_tensor.shape[1] * binary_tensor.shape[2]])\n",
    "\n",
    "sparse_mat = np.multiply(dense_mat, binary_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 6.54248\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 5.76746\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 5.7331\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 5.74967\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 5.48408\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 5.36829\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 4.93222\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 4.70856\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 4.66498\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 4.74202\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: 4.69944\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: 4.64699\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: 4.58376\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: 4.56541\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: 4.57934\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: 4.53475\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: 4.54741\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: 4.60075\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: 4.63094\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: 4.59308\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: 4.5828\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: 4.54219\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: 4.51025\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: 4.482\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: 4.46875\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: 4.46078\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: 4.45712\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: 4.45436\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: 4.4563\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: 4.45248\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: 4.45449\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: 4.45683\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: 4.4544\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: 4.45835\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: 4.46065\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: 4.45809\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: 4.46387\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: 4.4565\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: 4.46289\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: 4.46492\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: 4.46722\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: 4.46884\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: 4.46624\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: 4.4711\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: 4.47314\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: 4.47297\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: 4.47793\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: 4.47917\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: 4.48087\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: 4.48217\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: 4.48399\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: 4.48549\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: 4.48188\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: 4.48285\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: 4.48434\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: 4.48593\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: 4.49323\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: 4.48787\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: 4.49444\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: 4.49477\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: 4.49183\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: 4.48968\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: 4.49057\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: 4.49384\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: 4.49177\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: 4.49185\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: 4.49192\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: 4.48892\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: 4.48786\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: 4.49479\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: 4.49446\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: 4.49888\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: 4.49949\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: 4.49848\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: 4.49856\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: 4.49747\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: 4.50231\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: 4.49866\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: 4.49953\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: 4.49757\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: 4.49981\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: 4.49921\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: 4.49948\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: 4.49625\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: 4.50165\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: 4.50148\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: 4.50663\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: 4.50327\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: 4.50887\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: 4.50576\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: 4.5023\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: 4.50629\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: 4.50923\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: 4.51307\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: 4.50818\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: 4.50953\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: 4.50612\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: 4.50728\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: 4.50728\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: 4.50946\n",
      "\n",
      "Iteration: 101\n",
      "RMSE: 4.50996\n",
      "\n",
      "Iteration: 102\n",
      "RMSE: 4.51108\n",
      "\n",
      "Iteration: 103\n",
      "RMSE: 4.5158\n",
      "\n",
      "Iteration: 104\n",
      "RMSE: 4.51864\n",
      "\n",
      "Iteration: 105\n",
      "RMSE: 4.51461\n",
      "\n",
      "Iteration: 106\n",
      "RMSE: 4.51631\n",
      "\n",
      "Iteration: 107\n",
      "RMSE: 4.509\n",
      "\n",
      "Iteration: 108\n",
      "RMSE: 4.50882\n",
      "\n",
      "Iteration: 109\n",
      "RMSE: 4.51614\n",
      "\n",
      "Iteration: 110\n",
      "RMSE: 4.51157\n",
      "\n",
      "Iteration: 111\n",
      "RMSE: 4.51044\n",
      "\n",
      "Iteration: 112\n",
      "RMSE: 4.50869\n",
      "\n",
      "Iteration: 113\n",
      "RMSE: 4.50927\n",
      "\n",
      "Iteration: 114\n",
      "RMSE: 4.50959\n",
      "\n",
      "Iteration: 115\n",
      "RMSE: 4.51389\n",
      "\n",
      "Iteration: 116\n",
      "RMSE: 4.51256\n",
      "\n",
      "Iteration: 117\n",
      "RMSE: 4.51325\n",
      "\n",
      "Iteration: 118\n",
      "RMSE: 4.50974\n",
      "\n",
      "Iteration: 119\n",
      "RMSE: 4.51655\n",
      "\n",
      "Iteration: 120\n",
      "RMSE: 4.5115\n",
      "\n",
      "Iteration: 121\n",
      "RMSE: 4.51645\n",
      "\n",
      "Iteration: 122\n",
      "RMSE: 4.51753\n",
      "\n",
      "Iteration: 123\n",
      "RMSE: 4.51597\n",
      "\n",
      "Iteration: 124\n",
      "RMSE: 4.51971\n",
      "\n",
      "Iteration: 125\n",
      "RMSE: 4.52052\n",
      "\n",
      "Iteration: 126\n",
      "RMSE: 4.51515\n",
      "\n",
      "Iteration: 127\n",
      "RMSE: 4.51936\n",
      "\n",
      "Iteration: 128\n",
      "RMSE: 4.52494\n",
      "\n",
      "Iteration: 129\n",
      "RMSE: 4.52475\n",
      "\n",
      "Iteration: 130\n",
      "RMSE: 4.52563\n",
      "\n",
      "Iteration: 131\n",
      "RMSE: 4.5213\n",
      "\n",
      "Iteration: 132\n",
      "RMSE: 4.51497\n",
      "\n",
      "Iteration: 133\n",
      "RMSE: 4.50955\n",
      "\n",
      "Iteration: 134\n",
      "RMSE: 4.51106\n",
      "\n",
      "Iteration: 135\n",
      "RMSE: 4.51367\n",
      "\n",
      "Iteration: 136\n",
      "RMSE: 4.51811\n",
      "\n",
      "Iteration: 137\n",
      "RMSE: 4.51519\n",
      "\n",
      "Iteration: 138\n",
      "RMSE: 4.5184\n",
      "\n",
      "Iteration: 139\n",
      "RMSE: 4.51618\n",
      "\n",
      "Iteration: 140\n",
      "RMSE: 4.51715\n",
      "\n",
      "Iteration: 141\n",
      "RMSE: 4.5148\n",
      "\n",
      "Iteration: 142\n",
      "RMSE: 4.51163\n",
      "\n",
      "Iteration: 143\n",
      "RMSE: 4.51101\n",
      "\n",
      "Iteration: 144\n",
      "RMSE: 4.50948\n",
      "\n",
      "Iteration: 145\n",
      "RMSE: 4.50372\n",
      "\n",
      "Iteration: 146\n",
      "RMSE: 4.50677\n",
      "\n",
      "Iteration: 147\n",
      "RMSE: 4.51051\n",
      "\n",
      "Iteration: 148\n",
      "RMSE: 4.51091\n",
      "\n",
      "Iteration: 149\n",
      "RMSE: 4.512\n",
      "\n",
      "Iteration: 150\n",
      "RMSE: 4.51022\n",
      "\n",
      "Iteration: 151\n",
      "RMSE: 4.51022\n",
      "\n",
      "Iteration: 152\n",
      "RMSE: 4.50981\n",
      "\n",
      "Iteration: 153\n",
      "RMSE: 4.51303\n",
      "\n",
      "Iteration: 154\n",
      "RMSE: 4.51394\n",
      "\n",
      "Iteration: 155\n",
      "RMSE: 4.51371\n",
      "\n",
      "Iteration: 156\n",
      "RMSE: 4.50995\n",
      "\n",
      "Iteration: 157\n",
      "RMSE: 4.51253\n",
      "\n",
      "Iteration: 158\n",
      "RMSE: 4.51617\n",
      "\n",
      "Iteration: 159\n",
      "RMSE: 4.51278\n",
      "\n",
      "Iteration: 160\n",
      "RMSE: 4.52169\n",
      "\n",
      "Iteration: 161\n",
      "RMSE: 4.52016\n",
      "\n",
      "Iteration: 162\n",
      "RMSE: 4.51821\n",
      "\n",
      "Iteration: 163\n",
      "RMSE: 4.51732\n",
      "\n",
      "Iteration: 164\n",
      "RMSE: 4.51899\n",
      "\n",
      "Iteration: 165\n",
      "RMSE: 4.52507\n",
      "\n",
      "Iteration: 166\n",
      "RMSE: 4.5249\n",
      "\n",
      "Iteration: 167\n",
      "RMSE: 4.52547\n",
      "\n",
      "Iteration: 168\n",
      "RMSE: 4.52445\n",
      "\n",
      "Iteration: 169\n",
      "RMSE: 4.52202\n",
      "\n",
      "Iteration: 170\n",
      "RMSE: 4.52317\n",
      "\n",
      "Iteration: 171\n",
      "RMSE: 4.52458\n",
      "\n",
      "Iteration: 172\n",
      "RMSE: 4.52301\n",
      "\n",
      "Iteration: 173\n",
      "RMSE: 4.52225\n",
      "\n",
      "Iteration: 174\n",
      "RMSE: 4.5229\n",
      "\n",
      "Iteration: 175\n",
      "RMSE: 4.51735\n",
      "\n",
      "Iteration: 176\n",
      "RMSE: 4.5254\n",
      "\n",
      "Iteration: 177\n",
      "RMSE: 4.51979\n",
      "\n",
      "Iteration: 178\n",
      "RMSE: 4.52697\n",
      "\n",
      "Iteration: 179\n",
      "RMSE: 4.51904\n",
      "\n",
      "Iteration: 180\n",
      "RMSE: 4.51799\n",
      "\n",
      "Iteration: 181\n",
      "RMSE: 4.52044\n",
      "\n",
      "Iteration: 182\n",
      "RMSE: 4.52175\n",
      "\n",
      "Iteration: 183\n",
      "RMSE: 4.52076\n",
      "\n",
      "Iteration: 184\n",
      "RMSE: 4.5163\n",
      "\n",
      "Iteration: 185\n",
      "RMSE: 4.51807\n",
      "\n",
      "Iteration: 186\n",
      "RMSE: 4.51643\n",
      "\n",
      "Iteration: 187\n",
      "RMSE: 4.521\n",
      "\n",
      "Iteration: 188\n",
      "RMSE: 4.52175\n",
      "\n",
      "Iteration: 189\n",
      "RMSE: 4.51775\n",
      "\n",
      "Iteration: 190\n",
      "RMSE: 4.51784\n",
      "\n",
      "Iteration: 191\n",
      "RMSE: 4.51418\n",
      "\n",
      "Iteration: 192\n",
      "RMSE: 4.51654\n",
      "\n",
      "Iteration: 193\n",
      "RMSE: 4.51179\n",
      "\n",
      "Iteration: 194\n",
      "RMSE: 4.51213\n",
      "\n",
      "Iteration: 195\n",
      "RMSE: 4.50986\n",
      "\n",
      "Iteration: 196\n",
      "RMSE: 4.51197\n",
      "\n",
      "Iteration: 197\n",
      "RMSE: 4.51769\n",
      "\n",
      "Iteration: 198\n",
      "RMSE: 4.51498\n",
      "\n",
      "Iteration: 199\n",
      "RMSE: 4.51622\n",
      "\n",
      "Iteration: 200\n",
      "RMSE: 4.51443\n",
      "\n",
      "Iteration: 201\n",
      "RMSE: 4.51696\n",
      "\n",
      "Iteration: 202\n",
      "RMSE: 4.51898\n",
      "\n",
      "Iteration: 203\n",
      "RMSE: 4.51956\n",
      "\n",
      "Iteration: 204\n",
      "RMSE: 4.52316\n",
      "\n",
      "Iteration: 205\n",
      "RMSE: 4.51832\n",
      "\n",
      "Iteration: 206\n",
      "RMSE: 4.51886\n",
      "\n",
      "Iteration: 207\n",
      "RMSE: 4.52576\n",
      "\n",
      "Iteration: 208\n",
      "RMSE: 4.5217\n",
      "\n",
      "Iteration: 209\n",
      "RMSE: 4.5252\n",
      "\n",
      "Iteration: 210\n",
      "RMSE: 4.5261\n",
      "\n",
      "Iteration: 211\n",
      "RMSE: 4.52519\n",
      "\n",
      "Iteration: 212\n",
      "RMSE: 4.52557\n",
      "\n",
      "Iteration: 213\n",
      "RMSE: 4.52475\n",
      "\n",
      "Iteration: 214\n",
      "RMSE: 4.52106\n",
      "\n",
      "Iteration: 215\n",
      "RMSE: 4.52829\n",
      "\n",
      "Iteration: 216\n",
      "RMSE: 4.53196\n",
      "\n",
      "Iteration: 217\n",
      "RMSE: 4.52872\n",
      "\n",
      "Iteration: 218\n",
      "RMSE: 4.53156\n",
      "\n",
      "Iteration: 219\n",
      "RMSE: 4.52768\n",
      "\n",
      "Iteration: 220\n",
      "RMSE: 4.52834\n",
      "\n",
      "Iteration: 221\n",
      "RMSE: 4.53278\n",
      "\n",
      "Iteration: 222\n",
      "RMSE: 4.53164\n",
      "\n",
      "Iteration: 223\n",
      "RMSE: 4.52732\n",
      "\n",
      "Iteration: 224\n",
      "RMSE: 4.53258\n",
      "\n",
      "Iteration: 225\n",
      "RMSE: 4.52714\n",
      "\n",
      "Iteration: 226\n",
      "RMSE: 4.52354\n",
      "\n",
      "Iteration: 227\n",
      "RMSE: 4.52532\n",
      "\n",
      "Iteration: 228\n",
      "RMSE: 4.52041\n",
      "\n",
      "Iteration: 229\n",
      "RMSE: 4.52318\n",
      "\n",
      "Iteration: 230\n",
      "RMSE: 4.51986\n",
      "\n",
      "Iteration: 231\n",
      "RMSE: 4.52249\n",
      "\n",
      "Iteration: 232\n",
      "RMSE: 4.52028\n",
      "\n",
      "Iteration: 233\n",
      "RMSE: 4.52147\n",
      "\n",
      "Iteration: 234\n",
      "RMSE: 4.51878\n",
      "\n",
      "Iteration: 235\n",
      "RMSE: 4.52191\n",
      "\n",
      "Iteration: 236\n",
      "RMSE: 4.52596\n",
      "\n",
      "Iteration: 237\n",
      "RMSE: 4.52439\n",
      "\n",
      "Iteration: 238\n",
      "RMSE: 4.52472\n",
      "\n",
      "Iteration: 239\n",
      "RMSE: 4.52445\n",
      "\n",
      "Iteration: 240\n",
      "RMSE: 4.525\n",
      "\n",
      "Iteration: 241\n",
      "RMSE: 4.52026\n",
      "\n",
      "Iteration: 242\n",
      "RMSE: 4.52282\n",
      "\n",
      "Iteration: 243\n",
      "RMSE: 4.5235\n",
      "\n",
      "Iteration: 244\n",
      "RMSE: 4.52011\n",
      "\n",
      "Iteration: 245\n",
      "RMSE: 4.52712\n",
      "\n",
      "Iteration: 246\n",
      "RMSE: 4.52684\n",
      "\n",
      "Iteration: 247\n",
      "RMSE: 4.52991\n",
      "\n",
      "Iteration: 248\n",
      "RMSE: 4.52969\n",
      "\n",
      "Iteration: 249\n",
      "RMSE: 4.53143\n",
      "\n",
      "Iteration: 250\n",
      "RMSE: 4.51897\n",
      "\n",
      "Iteration: 251\n",
      "RMSE: 4.52219\n",
      "\n",
      "Iteration: 252\n",
      "RMSE: 4.52754\n",
      "\n",
      "Iteration: 253\n",
      "RMSE: 4.52623\n",
      "\n",
      "Iteration: 254\n",
      "RMSE: 4.52428\n",
      "\n",
      "Iteration: 255\n",
      "RMSE: 4.53503\n",
      "\n",
      "Iteration: 256\n",
      "RMSE: 4.53656\n",
      "\n",
      "Iteration: 257\n",
      "RMSE: 4.53299\n",
      "\n",
      "Iteration: 258\n",
      "RMSE: 4.52972\n",
      "\n",
      "Iteration: 259\n",
      "RMSE: 4.5281\n",
      "\n",
      "Iteration: 260\n",
      "RMSE: 4.52628\n",
      "\n",
      "Iteration: 261\n",
      "RMSE: 4.52702\n",
      "\n",
      "Iteration: 262\n",
      "RMSE: 4.52688\n",
      "\n",
      "Iteration: 263\n",
      "RMSE: 4.52302\n",
      "\n",
      "Iteration: 264\n",
      "RMSE: 4.52649\n",
      "\n",
      "Iteration: 265\n",
      "RMSE: 4.52815\n",
      "\n",
      "Iteration: 266\n",
      "RMSE: 4.52705\n",
      "\n",
      "Iteration: 267\n",
      "RMSE: 4.52549\n",
      "\n",
      "Iteration: 268\n",
      "RMSE: 4.52887\n",
      "\n",
      "Iteration: 269\n",
      "RMSE: 4.52597\n",
      "\n",
      "Iteration: 270\n",
      "RMSE: 4.52783\n",
      "\n",
      "Iteration: 271\n",
      "RMSE: 4.52954\n",
      "\n",
      "Iteration: 272\n",
      "RMSE: 4.52559\n",
      "\n",
      "Iteration: 273\n",
      "RMSE: 4.5254\n",
      "\n",
      "Iteration: 274\n",
      "RMSE: 4.53485\n",
      "\n",
      "Iteration: 275\n",
      "RMSE: 4.53453\n",
      "\n",
      "Iteration: 276\n",
      "RMSE: 4.53197\n",
      "\n",
      "Iteration: 277\n",
      "RMSE: 4.53227\n",
      "\n",
      "Iteration: 278\n",
      "RMSE: 4.53732\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 279\n",
      "RMSE: 4.5352\n",
      "\n",
      "Iteration: 280\n",
      "RMSE: 4.53879\n",
      "\n",
      "Iteration: 281\n",
      "RMSE: 4.53062\n",
      "\n",
      "Iteration: 282\n",
      "RMSE: 4.53645\n",
      "\n",
      "Iteration: 283\n",
      "RMSE: 4.53852\n",
      "\n",
      "Iteration: 284\n",
      "RMSE: 4.53585\n",
      "\n",
      "Iteration: 285\n",
      "RMSE: 4.52965\n",
      "\n",
      "Iteration: 286\n",
      "RMSE: 4.5337\n",
      "\n",
      "Iteration: 287\n",
      "RMSE: 4.52432\n",
      "\n",
      "Iteration: 288\n",
      "RMSE: 4.5294\n",
      "\n",
      "Iteration: 289\n",
      "RMSE: 4.53376\n",
      "\n",
      "Iteration: 290\n",
      "RMSE: 4.52812\n",
      "\n",
      "Iteration: 291\n",
      "RMSE: 4.5261\n",
      "\n",
      "Iteration: 292\n",
      "RMSE: 4.5263\n",
      "\n",
      "Iteration: 293\n",
      "RMSE: 4.52704\n",
      "\n",
      "Iteration: 294\n",
      "RMSE: 4.52451\n",
      "\n",
      "Iteration: 295\n",
      "RMSE: 4.52665\n",
      "\n",
      "Iteration: 296\n",
      "RMSE: 4.52461\n",
      "\n",
      "Iteration: 297\n",
      "RMSE: 4.52631\n",
      "\n",
      "Iteration: 298\n",
      "RMSE: 4.51936\n",
      "\n",
      "Iteration: 299\n",
      "RMSE: 4.52083\n",
      "\n",
      "Iteration: 300\n",
      "RMSE: 4.51877\n",
      "\n",
      "Iteration: 301\n",
      "RMSE: 4.52033\n",
      "\n",
      "Iteration: 302\n",
      "RMSE: 4.52117\n",
      "\n",
      "Iteration: 303\n",
      "RMSE: 4.52341\n",
      "\n",
      "Iteration: 304\n",
      "RMSE: 4.52289\n",
      "\n",
      "Iteration: 305\n",
      "RMSE: 4.52642\n",
      "\n",
      "Iteration: 306\n",
      "RMSE: 4.52659\n",
      "\n",
      "Iteration: 307\n",
      "RMSE: 4.52489\n",
      "\n",
      "Iteration: 308\n",
      "RMSE: 4.51955\n",
      "\n",
      "Iteration: 309\n",
      "RMSE: 4.52345\n",
      "\n",
      "Iteration: 310\n",
      "RMSE: 4.52159\n",
      "\n",
      "Iteration: 311\n",
      "RMSE: 4.52437\n",
      "\n",
      "Iteration: 312\n",
      "RMSE: 4.52354\n",
      "\n",
      "Iteration: 313\n",
      "RMSE: 4.52731\n",
      "\n",
      "Iteration: 314\n",
      "RMSE: 4.52163\n",
      "\n",
      "Iteration: 315\n",
      "RMSE: 4.52916\n",
      "\n",
      "Iteration: 316\n",
      "RMSE: 4.53132\n",
      "\n",
      "Iteration: 317\n",
      "RMSE: 4.5321\n",
      "\n",
      "Iteration: 318\n",
      "RMSE: 4.5296\n",
      "\n",
      "Iteration: 319\n",
      "RMSE: 4.53563\n",
      "\n",
      "Iteration: 320\n",
      "RMSE: 4.53643\n",
      "\n",
      "Iteration: 321\n",
      "RMSE: 4.52883\n",
      "\n",
      "Iteration: 322\n",
      "RMSE: 4.53063\n",
      "\n",
      "Iteration: 323\n",
      "RMSE: 4.53079\n",
      "\n",
      "Iteration: 324\n",
      "RMSE: 4.52998\n",
      "\n",
      "Iteration: 325\n",
      "RMSE: 4.53215\n",
      "\n",
      "Iteration: 326\n",
      "RMSE: 4.52885\n",
      "\n",
      "Iteration: 327\n",
      "RMSE: 4.52988\n",
      "\n",
      "Iteration: 328\n",
      "RMSE: 4.52789\n",
      "\n",
      "Iteration: 329\n",
      "RMSE: 4.52612\n",
      "\n",
      "Iteration: 330\n",
      "RMSE: 4.53023\n",
      "\n",
      "Iteration: 331\n",
      "RMSE: 4.52489\n",
      "\n",
      "Iteration: 332\n",
      "RMSE: 4.53017\n",
      "\n",
      "Iteration: 333\n",
      "RMSE: 4.52457\n",
      "\n",
      "Iteration: 334\n",
      "RMSE: 4.51781\n",
      "\n",
      "Iteration: 335\n",
      "RMSE: 4.5236\n",
      "\n",
      "Iteration: 336\n",
      "RMSE: 4.52071\n",
      "\n",
      "Iteration: 337\n",
      "RMSE: 4.52232\n",
      "\n",
      "Iteration: 338\n",
      "RMSE: 4.52527\n",
      "\n",
      "Iteration: 339\n",
      "RMSE: 4.51647\n",
      "\n",
      "Iteration: 340\n",
      "RMSE: 4.5226\n",
      "\n",
      "Iteration: 341\n",
      "RMSE: 4.52087\n",
      "\n",
      "Iteration: 342\n",
      "RMSE: 4.51478\n",
      "\n",
      "Iteration: 343\n",
      "RMSE: 4.51801\n",
      "\n",
      "Iteration: 344\n",
      "RMSE: 4.51371\n",
      "\n",
      "Iteration: 345\n",
      "RMSE: 4.51591\n",
      "\n",
      "Iteration: 346\n",
      "RMSE: 4.52391\n",
      "\n",
      "Iteration: 347\n",
      "RMSE: 4.52513\n",
      "\n",
      "Iteration: 348\n",
      "RMSE: 4.5226\n",
      "\n",
      "Iteration: 349\n",
      "RMSE: 4.52642\n",
      "\n",
      "Iteration: 350\n",
      "RMSE: 4.52443\n",
      "\n",
      "Iteration: 351\n",
      "RMSE: 4.52426\n",
      "\n",
      "Iteration: 352\n",
      "RMSE: 4.52348\n",
      "\n",
      "Iteration: 353\n",
      "RMSE: 4.52185\n",
      "\n",
      "Iteration: 354\n",
      "RMSE: 4.5259\n",
      "\n",
      "Iteration: 355\n",
      "RMSE: 4.52545\n",
      "\n",
      "Iteration: 356\n",
      "RMSE: 4.52195\n",
      "\n",
      "Iteration: 357\n",
      "RMSE: 4.51736\n",
      "\n",
      "Iteration: 358\n",
      "RMSE: 4.52086\n",
      "\n",
      "Iteration: 359\n",
      "RMSE: 4.51767\n",
      "\n",
      "Iteration: 360\n",
      "RMSE: 4.52084\n",
      "\n",
      "Iteration: 361\n",
      "RMSE: 4.52417\n",
      "\n",
      "Iteration: 362\n",
      "RMSE: 4.52255\n",
      "\n",
      "Iteration: 363\n",
      "RMSE: 4.51977\n",
      "\n",
      "Iteration: 364\n",
      "RMSE: 4.5217\n",
      "\n",
      "Iteration: 365\n",
      "RMSE: 4.5242\n",
      "\n",
      "Iteration: 366\n",
      "RMSE: 4.52695\n",
      "\n",
      "Iteration: 367\n",
      "RMSE: 4.52257\n",
      "\n",
      "Iteration: 368\n",
      "RMSE: 4.5255\n",
      "\n",
      "Iteration: 369\n",
      "RMSE: 4.52872\n",
      "\n",
      "Iteration: 370\n",
      "RMSE: 4.52941\n",
      "\n",
      "Iteration: 371\n",
      "RMSE: 4.52717\n",
      "\n",
      "Iteration: 372\n",
      "RMSE: 4.52902\n",
      "\n",
      "Iteration: 373\n",
      "RMSE: 4.52998\n",
      "\n",
      "Iteration: 374\n",
      "RMSE: 4.52738\n",
      "\n",
      "Iteration: 375\n",
      "RMSE: 4.52985\n",
      "\n",
      "Iteration: 376\n",
      "RMSE: 4.52792\n",
      "\n",
      "Iteration: 377\n",
      "RMSE: 4.53206\n",
      "\n",
      "Iteration: 378\n",
      "RMSE: 4.53315\n",
      "\n",
      "Iteration: 379\n",
      "RMSE: 4.53134\n",
      "\n",
      "Iteration: 380\n",
      "RMSE: 4.53562\n",
      "\n",
      "Iteration: 381\n",
      "RMSE: 4.53507\n",
      "\n",
      "Iteration: 382\n",
      "RMSE: 4.53692\n",
      "\n",
      "Iteration: 383\n",
      "RMSE: 4.53146\n",
      "\n",
      "Iteration: 384\n",
      "RMSE: 4.53446\n",
      "\n",
      "Iteration: 385\n",
      "RMSE: 4.53091\n",
      "\n",
      "Iteration: 386\n",
      "RMSE: 4.5357\n",
      "\n",
      "Iteration: 387\n",
      "RMSE: 4.53309\n",
      "\n",
      "Iteration: 388\n",
      "RMSE: 4.53531\n",
      "\n",
      "Iteration: 389\n",
      "RMSE: 4.54061\n",
      "\n",
      "Iteration: 390\n",
      "RMSE: 4.53918\n",
      "\n",
      "Iteration: 391\n",
      "RMSE: 4.53562\n",
      "\n",
      "Iteration: 392\n",
      "RMSE: 4.53603\n",
      "\n",
      "Iteration: 393\n",
      "RMSE: 4.52891\n",
      "\n",
      "Iteration: 394\n",
      "RMSE: 4.532\n",
      "\n",
      "Iteration: 395\n",
      "RMSE: 4.53347\n",
      "\n",
      "Iteration: 396\n",
      "RMSE: 4.53356\n",
      "\n",
      "Iteration: 397\n",
      "RMSE: 4.53255\n",
      "\n",
      "Iteration: 398\n",
      "RMSE: 4.53476\n",
      "\n",
      "Iteration: 399\n",
      "RMSE: 4.53475\n",
      "\n",
      "Iteration: 400\n",
      "RMSE: 4.52886\n",
      "\n",
      "Iteration: 401\n",
      "RMSE: 4.52994\n",
      "\n",
      "Iteration: 402\n",
      "RMSE: 4.52655\n",
      "\n",
      "Iteration: 403\n",
      "RMSE: 4.53032\n",
      "\n",
      "Iteration: 404\n",
      "RMSE: 4.52539\n",
      "\n",
      "Iteration: 405\n",
      "RMSE: 4.52453\n",
      "\n",
      "Iteration: 406\n",
      "RMSE: 4.52824\n",
      "\n",
      "Iteration: 407\n",
      "RMSE: 4.53087\n",
      "\n",
      "Iteration: 408\n",
      "RMSE: 4.52986\n",
      "\n",
      "Iteration: 409\n",
      "RMSE: 4.52777\n",
      "\n",
      "Iteration: 410\n",
      "RMSE: 4.53172\n",
      "\n",
      "Iteration: 411\n",
      "RMSE: 4.53029\n",
      "\n",
      "Iteration: 412\n",
      "RMSE: 4.53078\n",
      "\n",
      "Iteration: 413\n",
      "RMSE: 4.52824\n",
      "\n",
      "Iteration: 414\n",
      "RMSE: 4.52678\n",
      "\n",
      "Iteration: 415\n",
      "RMSE: 4.52826\n",
      "\n",
      "Iteration: 416\n",
      "RMSE: 4.52866\n",
      "\n",
      "Iteration: 417\n",
      "RMSE: 4.52841\n",
      "\n",
      "Iteration: 418\n",
      "RMSE: 4.52684\n",
      "\n",
      "Iteration: 419\n",
      "RMSE: 4.52831\n",
      "\n",
      "Iteration: 420\n",
      "RMSE: 4.5276\n",
      "\n",
      "Iteration: 421\n",
      "RMSE: 4.52809\n",
      "\n",
      "Iteration: 422\n",
      "RMSE: 4.52785\n",
      "\n",
      "Iteration: 423\n",
      "RMSE: 4.52665\n",
      "\n",
      "Iteration: 424\n",
      "RMSE: 4.52958\n",
      "\n",
      "Iteration: 425\n",
      "RMSE: 4.52598\n",
      "\n",
      "Iteration: 426\n",
      "RMSE: 4.52429\n",
      "\n",
      "Iteration: 427\n",
      "RMSE: 4.52721\n",
      "\n",
      "Iteration: 428\n",
      "RMSE: 4.52759\n",
      "\n",
      "Iteration: 429\n",
      "RMSE: 4.52677\n",
      "\n",
      "Iteration: 430\n",
      "RMSE: 4.52952\n",
      "\n",
      "Iteration: 431\n",
      "RMSE: 4.52845\n",
      "\n",
      "Iteration: 432\n",
      "RMSE: 4.53172\n",
      "\n",
      "Iteration: 433\n",
      "RMSE: 4.52989\n",
      "\n",
      "Iteration: 434\n",
      "RMSE: 4.5319\n",
      "\n",
      "Iteration: 435\n",
      "RMSE: 4.53024\n",
      "\n",
      "Iteration: 436\n",
      "RMSE: 4.53294\n",
      "\n",
      "Iteration: 437\n",
      "RMSE: 4.52975\n",
      "\n",
      "Iteration: 438\n",
      "RMSE: 4.53034\n",
      "\n",
      "Iteration: 439\n",
      "RMSE: 4.53403\n",
      "\n",
      "Iteration: 440\n",
      "RMSE: 4.52657\n",
      "\n",
      "Iteration: 441\n",
      "RMSE: 4.52537\n",
      "\n",
      "Iteration: 442\n",
      "RMSE: 4.52632\n",
      "\n",
      "Iteration: 443\n",
      "RMSE: 4.525\n",
      "\n",
      "Iteration: 444\n",
      "RMSE: 4.52483\n",
      "\n",
      "Iteration: 445\n",
      "RMSE: 4.52809\n",
      "\n",
      "Iteration: 446\n",
      "RMSE: 4.52304\n",
      "\n",
      "Iteration: 447\n",
      "RMSE: 4.51666\n",
      "\n",
      "Iteration: 448\n",
      "RMSE: 4.51913\n",
      "\n",
      "Iteration: 449\n",
      "RMSE: 4.52086\n",
      "\n",
      "Iteration: 450\n",
      "RMSE: 4.52373\n",
      "\n",
      "Iteration: 451\n",
      "RMSE: 4.52259\n",
      "\n",
      "Iteration: 452\n",
      "RMSE: 4.52086\n",
      "\n",
      "Iteration: 453\n",
      "RMSE: 4.52423\n",
      "\n",
      "Iteration: 454\n",
      "RMSE: 4.51958\n",
      "\n",
      "Iteration: 455\n",
      "RMSE: 4.52224\n",
      "\n",
      "Iteration: 456\n",
      "RMSE: 4.523\n",
      "\n",
      "Iteration: 457\n",
      "RMSE: 4.52758\n",
      "\n",
      "Iteration: 458\n",
      "RMSE: 4.52867\n",
      "\n",
      "Iteration: 459\n",
      "RMSE: 4.52593\n",
      "\n",
      "Iteration: 460\n",
      "RMSE: 4.52626\n",
      "\n",
      "Iteration: 461\n",
      "RMSE: 4.52714\n",
      "\n",
      "Iteration: 462\n",
      "RMSE: 4.52334\n",
      "\n",
      "Iteration: 463\n",
      "RMSE: 4.5271\n",
      "\n",
      "Iteration: 464\n",
      "RMSE: 4.53112\n",
      "\n",
      "Iteration: 465\n",
      "RMSE: 4.52943\n",
      "\n",
      "Iteration: 466\n",
      "RMSE: 4.5279\n",
      "\n",
      "Iteration: 467\n",
      "RMSE: 4.53\n",
      "\n",
      "Iteration: 468\n",
      "RMSE: 4.52898\n",
      "\n",
      "Iteration: 469\n",
      "RMSE: 4.53234\n",
      "\n",
      "Iteration: 470\n",
      "RMSE: 4.53738\n",
      "\n",
      "Iteration: 471\n",
      "RMSE: 4.53088\n",
      "\n",
      "Iteration: 472\n",
      "RMSE: 4.52802\n",
      "\n",
      "Iteration: 473\n",
      "RMSE: 4.52704\n",
      "\n",
      "Iteration: 474\n",
      "RMSE: 4.52213\n",
      "\n",
      "Iteration: 475\n",
      "RMSE: 4.5274\n",
      "\n",
      "Iteration: 476\n",
      "RMSE: 4.52198\n",
      "\n",
      "Iteration: 477\n",
      "RMSE: 4.52191\n",
      "\n",
      "Iteration: 478\n",
      "RMSE: 4.52346\n",
      "\n",
      "Iteration: 479\n",
      "RMSE: 4.52429\n",
      "\n",
      "Iteration: 480\n",
      "RMSE: 4.52095\n",
      "\n",
      "Iteration: 481\n",
      "RMSE: 4.52704\n",
      "\n",
      "Iteration: 482\n",
      "RMSE: 4.53436\n",
      "\n",
      "Iteration: 483\n",
      "RMSE: 4.52934\n",
      "\n",
      "Iteration: 484\n",
      "RMSE: 4.52894\n",
      "\n",
      "Iteration: 485\n",
      "RMSE: 4.52883\n",
      "\n",
      "Iteration: 486\n",
      "RMSE: 4.53024\n",
      "\n",
      "Iteration: 487\n",
      "RMSE: 4.53104\n",
      "\n",
      "Iteration: 488\n",
      "RMSE: 4.52468\n",
      "\n",
      "Iteration: 489\n",
      "RMSE: 4.52624\n",
      "\n",
      "Iteration: 490\n",
      "RMSE: 4.52493\n",
      "\n",
      "Iteration: 491\n",
      "RMSE: 4.52657\n",
      "\n",
      "Iteration: 492\n",
      "RMSE: 4.52444\n",
      "\n",
      "Iteration: 493\n",
      "RMSE: 4.52802\n",
      "\n",
      "Iteration: 494\n",
      "RMSE: 4.52425\n",
      "\n",
      "Iteration: 495\n",
      "RMSE: 4.52896\n",
      "\n",
      "Iteration: 496\n",
      "RMSE: 4.52695\n",
      "\n",
      "Iteration: 497\n",
      "RMSE: 4.53165\n",
      "\n",
      "Iteration: 498\n",
      "RMSE: 4.52803\n",
      "\n",
      "Iteration: 499\n",
      "RMSE: 4.52833\n",
      "\n",
      "Iteration: 500\n",
      "RMSE: 4.52886\n",
      "\n",
      "Iteration: 501\n",
      "RMSE: 4.5265\n",
      "\n",
      "Iteration: 502\n",
      "RMSE: 4.53043\n",
      "\n",
      "Iteration: 503\n",
      "RMSE: 4.53015\n",
      "\n",
      "Iteration: 504\n",
      "RMSE: 4.52619\n",
      "\n",
      "Iteration: 505\n",
      "RMSE: 4.52874\n",
      "\n",
      "Iteration: 506\n",
      "RMSE: 4.53217\n",
      "\n",
      "Iteration: 507\n",
      "RMSE: 4.52727\n",
      "\n",
      "Iteration: 508\n",
      "RMSE: 4.52778\n",
      "\n",
      "Iteration: 509\n",
      "RMSE: 4.52443\n",
      "\n",
      "Iteration: 510\n",
      "RMSE: 4.5266\n",
      "\n",
      "Iteration: 511\n",
      "RMSE: 4.53239\n",
      "\n",
      "Iteration: 512\n",
      "RMSE: 4.53004\n",
      "\n",
      "Iteration: 513\n",
      "RMSE: 4.53317\n",
      "\n",
      "Iteration: 514\n",
      "RMSE: 4.53468\n",
      "\n",
      "Iteration: 515\n",
      "RMSE: 4.53953\n",
      "\n",
      "Iteration: 516\n",
      "RMSE: 4.53206\n",
      "\n",
      "Iteration: 517\n",
      "RMSE: 4.53579\n",
      "\n",
      "Iteration: 518\n",
      "RMSE: 4.5304\n",
      "\n",
      "Iteration: 519\n",
      "RMSE: 4.52855\n",
      "\n",
      "Iteration: 520\n",
      "RMSE: 4.53703\n",
      "\n",
      "Iteration: 521\n",
      "RMSE: 4.53452\n",
      "\n",
      "Iteration: 522\n",
      "RMSE: 4.53407\n",
      "\n",
      "Iteration: 523\n",
      "RMSE: 4.53334\n",
      "\n",
      "Iteration: 524\n",
      "RMSE: 4.53168\n",
      "\n",
      "Iteration: 525\n",
      "RMSE: 4.53437\n",
      "\n",
      "Iteration: 526\n",
      "RMSE: 4.53955\n",
      "\n",
      "Iteration: 527\n",
      "RMSE: 4.53421\n",
      "\n",
      "Iteration: 528\n",
      "RMSE: 4.53459\n",
      "\n",
      "Iteration: 529\n",
      "RMSE: 4.53562\n",
      "\n",
      "Iteration: 530\n",
      "RMSE: 4.54047\n",
      "\n",
      "Iteration: 531\n",
      "RMSE: 4.54247\n",
      "\n",
      "Iteration: 532\n",
      "RMSE: 4.53641\n",
      "\n",
      "Iteration: 533\n",
      "RMSE: 4.53905\n",
      "\n",
      "Iteration: 534\n",
      "RMSE: 4.54087\n",
      "\n",
      "Iteration: 535\n",
      "RMSE: 4.53636\n",
      "\n",
      "Iteration: 536\n",
      "RMSE: 4.53788\n",
      "\n",
      "Iteration: 537\n",
      "RMSE: 4.53504\n",
      "\n",
      "Iteration: 538\n",
      "RMSE: 4.53872\n",
      "\n",
      "Iteration: 539\n",
      "RMSE: 4.53922\n",
      "\n",
      "Iteration: 540\n",
      "RMSE: 4.53894\n",
      "\n",
      "Iteration: 541\n",
      "RMSE: 4.53858\n",
      "\n",
      "Iteration: 542\n",
      "RMSE: 4.53996\n",
      "\n",
      "Iteration: 543\n",
      "RMSE: 4.54151\n",
      "\n",
      "Iteration: 544\n",
      "RMSE: 4.54145\n",
      "\n",
      "Iteration: 545\n",
      "RMSE: 4.54106\n",
      "\n",
      "Iteration: 546\n",
      "RMSE: 4.53761\n",
      "\n",
      "Iteration: 547\n",
      "RMSE: 4.53532\n",
      "\n",
      "Iteration: 548\n",
      "RMSE: 4.53868\n",
      "\n",
      "Iteration: 549\n",
      "RMSE: 4.5374\n",
      "\n",
      "Iteration: 550\n",
      "RMSE: 4.53311\n",
      "\n",
      "Iteration: 551\n",
      "RMSE: 4.53784\n",
      "\n",
      "Iteration: 552\n",
      "RMSE: 4.53647\n",
      "\n",
      "Iteration: 553\n",
      "RMSE: 4.53308\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 554\n",
      "RMSE: 4.53142\n",
      "\n",
      "Iteration: 555\n",
      "RMSE: 4.52967\n",
      "\n",
      "Iteration: 556\n",
      "RMSE: 4.52901\n",
      "\n",
      "Iteration: 557\n",
      "RMSE: 4.52616\n",
      "\n",
      "Iteration: 558\n",
      "RMSE: 4.5256\n",
      "\n",
      "Iteration: 559\n",
      "RMSE: 4.52306\n",
      "\n",
      "Iteration: 560\n",
      "RMSE: 4.52195\n",
      "\n",
      "Iteration: 561\n",
      "RMSE: 4.52115\n",
      "\n",
      "Iteration: 562\n",
      "RMSE: 4.53097\n",
      "\n",
      "Iteration: 563\n",
      "RMSE: 4.52992\n",
      "\n",
      "Iteration: 564\n",
      "RMSE: 4.52793\n",
      "\n",
      "Iteration: 565\n",
      "RMSE: 4.53062\n",
      "\n",
      "Iteration: 566\n",
      "RMSE: 4.52713\n",
      "\n",
      "Iteration: 567\n",
      "RMSE: 4.53011\n",
      "\n",
      "Iteration: 568\n",
      "RMSE: 4.52876\n",
      "\n",
      "Iteration: 569\n",
      "RMSE: 4.53496\n",
      "\n",
      "Iteration: 570\n",
      "RMSE: 4.53019\n",
      "\n",
      "Iteration: 571\n",
      "RMSE: 4.52878\n",
      "\n",
      "Iteration: 572\n",
      "RMSE: 4.5281\n",
      "\n",
      "Iteration: 573\n",
      "RMSE: 4.53244\n",
      "\n",
      "Iteration: 574\n",
      "RMSE: 4.52934\n",
      "\n",
      "Iteration: 575\n",
      "RMSE: 4.52825\n",
      "\n",
      "Iteration: 576\n",
      "RMSE: 4.53346\n",
      "\n",
      "Iteration: 577\n",
      "RMSE: 4.53242\n",
      "\n",
      "Iteration: 578\n",
      "RMSE: 4.53382\n",
      "\n",
      "Iteration: 579\n",
      "RMSE: 4.53286\n",
      "\n",
      "Iteration: 580\n",
      "RMSE: 4.53213\n",
      "\n",
      "Iteration: 581\n",
      "RMSE: 4.53003\n",
      "\n",
      "Iteration: 582\n",
      "RMSE: 4.52839\n",
      "\n",
      "Iteration: 583\n",
      "RMSE: 4.52916\n",
      "\n",
      "Iteration: 584\n",
      "RMSE: 4.53061\n",
      "\n",
      "Iteration: 585\n",
      "RMSE: 4.52901\n",
      "\n",
      "Iteration: 586\n",
      "RMSE: 4.53405\n",
      "\n",
      "Iteration: 587\n",
      "RMSE: 4.53424\n",
      "\n",
      "Iteration: 588\n",
      "RMSE: 4.53169\n",
      "\n",
      "Iteration: 589\n",
      "RMSE: 4.52615\n",
      "\n",
      "Iteration: 590\n",
      "RMSE: 4.52935\n",
      "\n",
      "Iteration: 591\n",
      "RMSE: 4.52739\n",
      "\n",
      "Iteration: 592\n",
      "RMSE: 4.53195\n",
      "\n",
      "Iteration: 593\n",
      "RMSE: 4.53024\n",
      "\n",
      "Iteration: 594\n",
      "RMSE: 4.53021\n",
      "\n",
      "Iteration: 595\n",
      "RMSE: 4.53175\n",
      "\n",
      "Iteration: 596\n",
      "RMSE: 4.52985\n",
      "\n",
      "Iteration: 597\n",
      "RMSE: 4.53102\n",
      "\n",
      "Iteration: 598\n",
      "RMSE: 4.52636\n",
      "\n",
      "Iteration: 599\n",
      "RMSE: 4.53202\n",
      "\n",
      "Iteration: 600\n",
      "RMSE: 4.5258\n",
      "\n",
      "Iteration: 601\n",
      "RMSE: 4.52745\n",
      "\n",
      "Iteration: 602\n",
      "RMSE: 4.51972\n",
      "\n",
      "Iteration: 603\n",
      "RMSE: 4.52381\n",
      "\n",
      "Iteration: 604\n",
      "RMSE: 4.52075\n",
      "\n",
      "Iteration: 605\n",
      "RMSE: 4.52824\n",
      "\n",
      "Iteration: 606\n",
      "RMSE: 4.52638\n",
      "\n",
      "Iteration: 607\n",
      "RMSE: 4.51942\n",
      "\n",
      "Iteration: 608\n",
      "RMSE: 4.52171\n",
      "\n",
      "Iteration: 609\n",
      "RMSE: 4.52829\n",
      "\n",
      "Iteration: 610\n",
      "RMSE: 4.52577\n",
      "\n",
      "Iteration: 611\n",
      "RMSE: 4.52418\n",
      "\n",
      "Iteration: 612\n",
      "RMSE: 4.52322\n",
      "\n",
      "Iteration: 613\n",
      "RMSE: 4.52642\n",
      "\n",
      "Iteration: 614\n",
      "RMSE: 4.52789\n",
      "\n",
      "Iteration: 615\n",
      "RMSE: 4.52859\n",
      "\n",
      "Iteration: 616\n",
      "RMSE: 4.52633\n",
      "\n",
      "Iteration: 617\n",
      "RMSE: 4.52544\n",
      "\n",
      "Iteration: 618\n",
      "RMSE: 4.52514\n",
      "\n",
      "Iteration: 619\n",
      "RMSE: 4.52644\n",
      "\n",
      "Iteration: 620\n",
      "RMSE: 4.53211\n",
      "\n",
      "Iteration: 621\n",
      "RMSE: 4.52624\n",
      "\n",
      "Iteration: 622\n",
      "RMSE: 4.53716\n",
      "\n",
      "Iteration: 623\n",
      "RMSE: 4.52543\n",
      "\n",
      "Iteration: 624\n",
      "RMSE: 4.52536\n",
      "\n",
      "Iteration: 625\n",
      "RMSE: 4.5277\n",
      "\n",
      "Iteration: 626\n",
      "RMSE: 4.52221\n",
      "\n",
      "Iteration: 627\n",
      "RMSE: 4.52674\n",
      "\n",
      "Iteration: 628\n",
      "RMSE: 4.52772\n",
      "\n",
      "Iteration: 629\n",
      "RMSE: 4.52888\n",
      "\n",
      "Iteration: 630\n",
      "RMSE: 4.52968\n",
      "\n",
      "Iteration: 631\n",
      "RMSE: 4.52842\n",
      "\n",
      "Iteration: 632\n",
      "RMSE: 4.53178\n",
      "\n",
      "Iteration: 633\n",
      "RMSE: 4.53182\n",
      "\n",
      "Iteration: 634\n",
      "RMSE: 4.53385\n",
      "\n",
      "Iteration: 635\n",
      "RMSE: 4.52912\n",
      "\n",
      "Iteration: 636\n",
      "RMSE: 4.53271\n",
      "\n",
      "Iteration: 637\n",
      "RMSE: 4.5326\n",
      "\n",
      "Iteration: 638\n",
      "RMSE: 4.5278\n",
      "\n",
      "Iteration: 639\n",
      "RMSE: 4.53181\n",
      "\n",
      "Iteration: 640\n",
      "RMSE: 4.52993\n",
      "\n",
      "Iteration: 641\n",
      "RMSE: 4.53449\n",
      "\n",
      "Iteration: 642\n",
      "RMSE: 4.52944\n",
      "\n",
      "Iteration: 643\n",
      "RMSE: 4.53202\n",
      "\n",
      "Iteration: 644\n",
      "RMSE: 4.52921\n",
      "\n",
      "Iteration: 645\n",
      "RMSE: 4.53377\n",
      "\n",
      "Iteration: 646\n",
      "RMSE: 4.52777\n",
      "\n",
      "Iteration: 647\n",
      "RMSE: 4.53272\n",
      "\n",
      "Iteration: 648\n",
      "RMSE: 4.52852\n",
      "\n",
      "Iteration: 649\n",
      "RMSE: 4.52956\n",
      "\n",
      "Iteration: 650\n",
      "RMSE: 4.52949\n",
      "\n",
      "Iteration: 651\n",
      "RMSE: 4.53218\n",
      "\n",
      "Iteration: 652\n",
      "RMSE: 4.53422\n",
      "\n",
      "Iteration: 653\n",
      "RMSE: 4.52896\n",
      "\n",
      "Iteration: 654\n",
      "RMSE: 4.52982\n",
      "\n",
      "Iteration: 655\n",
      "RMSE: 4.53125\n",
      "\n",
      "Iteration: 656\n",
      "RMSE: 4.52995\n",
      "\n",
      "Iteration: 657\n",
      "RMSE: 4.53204\n",
      "\n",
      "Iteration: 658\n",
      "RMSE: 4.52827\n",
      "\n",
      "Iteration: 659\n",
      "RMSE: 4.52993\n",
      "\n",
      "Iteration: 660\n",
      "RMSE: 4.52843\n",
      "\n",
      "Iteration: 661\n",
      "RMSE: 4.52466\n",
      "\n",
      "Iteration: 662\n",
      "RMSE: 4.53145\n",
      "\n",
      "Iteration: 663\n",
      "RMSE: 4.52921\n",
      "\n",
      "Iteration: 664\n",
      "RMSE: 4.53189\n",
      "\n",
      "Iteration: 665\n",
      "RMSE: 4.538\n",
      "\n",
      "Iteration: 666\n",
      "RMSE: 4.53556\n",
      "\n",
      "Iteration: 667\n",
      "RMSE: 4.53759\n",
      "\n",
      "Iteration: 668\n",
      "RMSE: 4.53156\n",
      "\n",
      "Iteration: 669\n",
      "RMSE: 4.52688\n",
      "\n",
      "Iteration: 670\n",
      "RMSE: 4.52716\n",
      "\n",
      "Iteration: 671\n",
      "RMSE: 4.52928\n",
      "\n",
      "Iteration: 672\n",
      "RMSE: 4.52819\n",
      "\n",
      "Iteration: 673\n",
      "RMSE: 4.53209\n",
      "\n",
      "Iteration: 674\n",
      "RMSE: 4.529\n",
      "\n",
      "Iteration: 675\n",
      "RMSE: 4.53476\n",
      "\n",
      "Iteration: 676\n",
      "RMSE: 4.53239\n",
      "\n",
      "Iteration: 677\n",
      "RMSE: 4.52864\n",
      "\n",
      "Iteration: 678\n",
      "RMSE: 4.53138\n",
      "\n",
      "Iteration: 679\n",
      "RMSE: 4.53058\n",
      "\n",
      "Iteration: 680\n",
      "RMSE: 4.53075\n",
      "\n",
      "Iteration: 681\n",
      "RMSE: 4.53052\n",
      "\n",
      "Iteration: 682\n",
      "RMSE: 4.52817\n",
      "\n",
      "Iteration: 683\n",
      "RMSE: 4.5321\n",
      "\n",
      "Iteration: 684\n",
      "RMSE: 4.52772\n",
      "\n",
      "Iteration: 685\n",
      "RMSE: 4.52689\n",
      "\n",
      "Iteration: 686\n",
      "RMSE: 4.53069\n",
      "\n",
      "Iteration: 687\n",
      "RMSE: 4.5321\n",
      "\n",
      "Iteration: 688\n",
      "RMSE: 4.53238\n",
      "\n",
      "Iteration: 689\n",
      "RMSE: 4.52893\n",
      "\n",
      "Iteration: 690\n",
      "RMSE: 4.53086\n",
      "\n",
      "Iteration: 691\n",
      "RMSE: 4.5339\n",
      "\n",
      "Iteration: 692\n",
      "RMSE: 4.52961\n",
      "\n",
      "Iteration: 693\n",
      "RMSE: 4.53223\n",
      "\n",
      "Iteration: 694\n",
      "RMSE: 4.53309\n",
      "\n",
      "Iteration: 695\n",
      "RMSE: 4.53002\n",
      "\n",
      "Iteration: 696\n",
      "RMSE: 4.53247\n",
      "\n",
      "Iteration: 697\n",
      "RMSE: 4.53161\n",
      "\n",
      "Iteration: 698\n",
      "RMSE: 4.52681\n",
      "\n",
      "Iteration: 699\n",
      "RMSE: 4.53073\n",
      "\n",
      "Iteration: 700\n",
      "RMSE: 4.53233\n",
      "\n",
      "Iteration: 701\n",
      "RMSE: 4.532\n",
      "\n",
      "Iteration: 702\n",
      "RMSE: 4.53403\n",
      "\n",
      "Iteration: 703\n",
      "RMSE: 4.53078\n",
      "\n",
      "Iteration: 704\n",
      "RMSE: 4.53706\n",
      "\n",
      "Iteration: 705\n",
      "RMSE: 4.53681\n",
      "\n",
      "Iteration: 706\n",
      "RMSE: 4.5351\n",
      "\n",
      "Iteration: 707\n",
      "RMSE: 4.53331\n",
      "\n",
      "Iteration: 708\n",
      "RMSE: 4.53511\n",
      "\n",
      "Iteration: 709\n",
      "RMSE: 4.54066\n",
      "\n",
      "Iteration: 710\n",
      "RMSE: 4.54084\n",
      "\n",
      "Iteration: 711\n",
      "RMSE: 4.53453\n",
      "\n",
      "Iteration: 712\n",
      "RMSE: 4.53941\n",
      "\n",
      "Iteration: 713\n",
      "RMSE: 4.54032\n",
      "\n",
      "Iteration: 714\n",
      "RMSE: 4.53667\n",
      "\n",
      "Iteration: 715\n",
      "RMSE: 4.53503\n",
      "\n",
      "Iteration: 716\n",
      "RMSE: 4.53776\n",
      "\n",
      "Iteration: 717\n",
      "RMSE: 4.53762\n",
      "\n",
      "Iteration: 718\n",
      "RMSE: 4.54009\n",
      "\n",
      "Iteration: 719\n",
      "RMSE: 4.53594\n",
      "\n",
      "Iteration: 720\n",
      "RMSE: 4.53677\n",
      "\n",
      "Iteration: 721\n",
      "RMSE: 4.53586\n",
      "\n",
      "Iteration: 722\n",
      "RMSE: 4.52967\n",
      "\n",
      "Iteration: 723\n",
      "RMSE: 4.53158\n",
      "\n",
      "Iteration: 724\n",
      "RMSE: 4.52934\n",
      "\n",
      "Iteration: 725\n",
      "RMSE: 4.53479\n",
      "\n",
      "Iteration: 726\n",
      "RMSE: 4.53863\n",
      "\n",
      "Iteration: 727\n",
      "RMSE: 4.53261\n",
      "\n",
      "Iteration: 728\n",
      "RMSE: 4.53745\n",
      "\n",
      "Iteration: 729\n",
      "RMSE: 4.53554\n",
      "\n",
      "Iteration: 730\n",
      "RMSE: 4.53565\n",
      "\n",
      "Iteration: 731\n",
      "RMSE: 4.53635\n",
      "\n",
      "Iteration: 732\n",
      "RMSE: 4.53439\n",
      "\n",
      "Iteration: 733\n",
      "RMSE: 4.53859\n",
      "\n",
      "Iteration: 734\n",
      "RMSE: 4.53381\n",
      "\n",
      "Iteration: 735\n",
      "RMSE: 4.53835\n",
      "\n",
      "Iteration: 736\n",
      "RMSE: 4.53386\n",
      "\n",
      "Iteration: 737\n",
      "RMSE: 4.52928\n",
      "\n",
      "Iteration: 738\n",
      "RMSE: 4.53142\n",
      "\n",
      "Iteration: 739\n",
      "RMSE: 4.53259\n",
      "\n",
      "Iteration: 740\n",
      "RMSE: 4.53116\n",
      "\n",
      "Iteration: 741\n",
      "RMSE: 4.53143\n",
      "\n",
      "Iteration: 742\n",
      "RMSE: 4.53251\n",
      "\n",
      "Iteration: 743\n",
      "RMSE: 4.52778\n",
      "\n",
      "Iteration: 744\n",
      "RMSE: 4.5266\n",
      "\n",
      "Iteration: 745\n",
      "RMSE: 4.53205\n",
      "\n",
      "Iteration: 746\n",
      "RMSE: 4.52854\n",
      "\n",
      "Iteration: 747\n",
      "RMSE: 4.52901\n",
      "\n",
      "Iteration: 748\n",
      "RMSE: 4.52818\n",
      "\n",
      "Iteration: 749\n",
      "RMSE: 4.52808\n",
      "\n",
      "Iteration: 750\n",
      "RMSE: 4.52765\n",
      "\n",
      "Iteration: 751\n",
      "RMSE: 4.52938\n",
      "\n",
      "Iteration: 752\n",
      "RMSE: 4.52935\n",
      "\n",
      "Iteration: 753\n",
      "RMSE: 4.52982\n",
      "\n",
      "Iteration: 754\n",
      "RMSE: 4.52737\n",
      "\n",
      "Iteration: 755\n",
      "RMSE: 4.52888\n",
      "\n",
      "Iteration: 756\n",
      "RMSE: 4.5248\n",
      "\n",
      "Iteration: 757\n",
      "RMSE: 4.5276\n",
      "\n",
      "Iteration: 758\n",
      "RMSE: 4.53045\n",
      "\n",
      "Iteration: 759\n",
      "RMSE: 4.52649\n",
      "\n",
      "Iteration: 760\n",
      "RMSE: 4.52516\n",
      "\n",
      "Iteration: 761\n",
      "RMSE: 4.5279\n",
      "\n",
      "Iteration: 762\n",
      "RMSE: 4.52506\n",
      "\n",
      "Iteration: 763\n",
      "RMSE: 4.52742\n",
      "\n",
      "Iteration: 764\n",
      "RMSE: 4.5259\n",
      "\n",
      "Iteration: 765\n",
      "RMSE: 4.52556\n",
      "\n",
      "Iteration: 766\n",
      "RMSE: 4.52728\n",
      "\n",
      "Iteration: 767\n",
      "RMSE: 4.52895\n",
      "\n",
      "Iteration: 768\n",
      "RMSE: 4.52796\n",
      "\n",
      "Iteration: 769\n",
      "RMSE: 4.52635\n",
      "\n",
      "Iteration: 770\n",
      "RMSE: 4.53237\n",
      "\n",
      "Iteration: 771\n",
      "RMSE: 4.53229\n",
      "\n",
      "Iteration: 772\n",
      "RMSE: 4.53328\n",
      "\n",
      "Iteration: 773\n",
      "RMSE: 4.53033\n",
      "\n",
      "Iteration: 774\n",
      "RMSE: 4.53227\n",
      "\n",
      "Iteration: 775\n",
      "RMSE: 4.52984\n",
      "\n",
      "Iteration: 776\n",
      "RMSE: 4.53046\n",
      "\n",
      "Iteration: 777\n",
      "RMSE: 4.53181\n",
      "\n",
      "Iteration: 778\n",
      "RMSE: 4.52834\n",
      "\n",
      "Iteration: 779\n",
      "RMSE: 4.5283\n",
      "\n",
      "Iteration: 780\n",
      "RMSE: 4.52956\n",
      "\n",
      "Iteration: 781\n",
      "RMSE: 4.53006\n",
      "\n",
      "Iteration: 782\n",
      "RMSE: 4.52947\n",
      "\n",
      "Iteration: 783\n",
      "RMSE: 4.53159\n",
      "\n",
      "Iteration: 784\n",
      "RMSE: 4.53054\n",
      "\n",
      "Iteration: 785\n",
      "RMSE: 4.5322\n",
      "\n",
      "Iteration: 786\n",
      "RMSE: 4.53251\n",
      "\n",
      "Iteration: 787\n",
      "RMSE: 4.53305\n",
      "\n",
      "Iteration: 788\n",
      "RMSE: 4.53242\n",
      "\n",
      "Iteration: 789\n",
      "RMSE: 4.53519\n",
      "\n",
      "Iteration: 790\n",
      "RMSE: 4.53574\n",
      "\n",
      "Iteration: 791\n",
      "RMSE: 4.53697\n",
      "\n",
      "Iteration: 792\n",
      "RMSE: 4.53377\n",
      "\n",
      "Iteration: 793\n",
      "RMSE: 4.53626\n",
      "\n",
      "Iteration: 794\n",
      "RMSE: 4.5319\n",
      "\n",
      "Iteration: 795\n",
      "RMSE: 4.52958\n",
      "\n",
      "Iteration: 796\n",
      "RMSE: 4.53134\n",
      "\n",
      "Iteration: 797\n",
      "RMSE: 4.52882\n",
      "\n",
      "Iteration: 798\n",
      "RMSE: 4.52978\n",
      "\n",
      "Iteration: 799\n",
      "RMSE: 4.53047\n",
      "\n",
      "Iteration: 800\n",
      "RMSE: 4.53358\n",
      "\n",
      "Iteration: 801\n",
      "RMSE: 4.52785\n",
      "\n",
      "Iteration: 802\n",
      "RMSE: 4.52874\n",
      "\n",
      "Iteration: 803\n",
      "RMSE: 4.52888\n",
      "\n",
      "Iteration: 804\n",
      "RMSE: 4.53159\n",
      "\n",
      "Iteration: 805\n",
      "RMSE: 4.5317\n",
      "\n",
      "Iteration: 806\n",
      "RMSE: 4.52803\n",
      "\n",
      "Iteration: 807\n",
      "RMSE: 4.53252\n",
      "\n",
      "Iteration: 808\n",
      "RMSE: 4.53031\n",
      "\n",
      "Iteration: 809\n",
      "RMSE: 4.5247\n",
      "\n",
      "Iteration: 810\n",
      "RMSE: 4.52764\n",
      "\n",
      "Iteration: 811\n",
      "RMSE: 4.52238\n",
      "\n",
      "Iteration: 812\n",
      "RMSE: 4.5245\n",
      "\n",
      "Iteration: 813\n",
      "RMSE: 4.52781\n",
      "\n",
      "Iteration: 814\n",
      "RMSE: 4.52699\n",
      "\n",
      "Iteration: 815\n",
      "RMSE: 4.5261\n",
      "\n",
      "Iteration: 816\n",
      "RMSE: 4.52934\n",
      "\n",
      "Iteration: 817\n",
      "RMSE: 4.52881\n",
      "\n",
      "Iteration: 818\n",
      "RMSE: 4.53071\n",
      "\n",
      "Iteration: 819\n",
      "RMSE: 4.52363\n",
      "\n",
      "Iteration: 820\n",
      "RMSE: 4.52889\n",
      "\n",
      "Iteration: 821\n",
      "RMSE: 4.52984\n",
      "\n",
      "Iteration: 822\n",
      "RMSE: 4.53265\n",
      "\n",
      "Iteration: 823\n",
      "RMSE: 4.53176\n",
      "\n",
      "Iteration: 824\n",
      "RMSE: 4.53325\n",
      "\n",
      "Iteration: 825\n",
      "RMSE: 4.52734\n",
      "\n",
      "Iteration: 826\n",
      "RMSE: 4.532\n",
      "\n",
      "Iteration: 827\n",
      "RMSE: 4.53267\n",
      "\n",
      "Iteration: 828\n",
      "RMSE: 4.52872\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 829\n",
      "RMSE: 4.52942\n",
      "\n",
      "Iteration: 830\n",
      "RMSE: 4.53005\n",
      "\n",
      "Iteration: 831\n",
      "RMSE: 4.53429\n",
      "\n",
      "Iteration: 832\n",
      "RMSE: 4.53\n",
      "\n",
      "Iteration: 833\n",
      "RMSE: 4.52923\n",
      "\n",
      "Iteration: 834\n",
      "RMSE: 4.52564\n",
      "\n",
      "Iteration: 835\n",
      "RMSE: 4.52425\n",
      "\n",
      "Iteration: 836\n",
      "RMSE: 4.52404\n",
      "\n",
      "Iteration: 837\n",
      "RMSE: 4.52049\n",
      "\n",
      "Iteration: 838\n",
      "RMSE: 4.52268\n",
      "\n",
      "Iteration: 839\n",
      "RMSE: 4.52179\n",
      "\n",
      "Iteration: 840\n",
      "RMSE: 4.52469\n",
      "\n",
      "Iteration: 841\n",
      "RMSE: 4.52052\n",
      "\n",
      "Iteration: 842\n",
      "RMSE: 4.52798\n",
      "\n",
      "Iteration: 843\n",
      "RMSE: 4.52719\n",
      "\n",
      "Iteration: 844\n",
      "RMSE: 4.52822\n",
      "\n",
      "Iteration: 845\n",
      "RMSE: 4.52859\n",
      "\n",
      "Iteration: 846\n",
      "RMSE: 4.52124\n",
      "\n",
      "Iteration: 847\n",
      "RMSE: 4.52414\n",
      "\n",
      "Iteration: 848\n",
      "RMSE: 4.52514\n",
      "\n",
      "Iteration: 849\n",
      "RMSE: 4.52461\n",
      "\n",
      "Iteration: 850\n",
      "RMSE: 4.5199\n",
      "\n",
      "Iteration: 851\n",
      "RMSE: 4.51987\n",
      "\n",
      "Iteration: 852\n",
      "RMSE: 4.5177\n",
      "\n",
      "Iteration: 853\n",
      "RMSE: 4.52069\n",
      "\n",
      "Iteration: 854\n",
      "RMSE: 4.52308\n",
      "\n",
      "Iteration: 855\n",
      "RMSE: 4.52469\n",
      "\n",
      "Iteration: 856\n",
      "RMSE: 4.52429\n",
      "\n",
      "Iteration: 857\n",
      "RMSE: 4.52416\n",
      "\n",
      "Iteration: 858\n",
      "RMSE: 4.52467\n",
      "\n",
      "Iteration: 859\n",
      "RMSE: 4.52621\n",
      "\n",
      "Iteration: 860\n",
      "RMSE: 4.52895\n",
      "\n",
      "Iteration: 861\n",
      "RMSE: 4.52379\n",
      "\n",
      "Iteration: 862\n",
      "RMSE: 4.52622\n",
      "\n",
      "Iteration: 863\n",
      "RMSE: 4.52564\n",
      "\n",
      "Iteration: 864\n",
      "RMSE: 4.5248\n",
      "\n",
      "Iteration: 865\n",
      "RMSE: 4.52622\n",
      "\n",
      "Iteration: 866\n",
      "RMSE: 4.52746\n",
      "\n",
      "Iteration: 867\n",
      "RMSE: 4.52238\n",
      "\n",
      "Iteration: 868\n",
      "RMSE: 4.51981\n",
      "\n",
      "Iteration: 869\n",
      "RMSE: 4.52142\n",
      "\n",
      "Iteration: 870\n",
      "RMSE: 4.52218\n",
      "\n",
      "Iteration: 871\n",
      "RMSE: 4.52303\n",
      "\n",
      "Iteration: 872\n",
      "RMSE: 4.51897\n",
      "\n",
      "Iteration: 873\n",
      "RMSE: 4.52221\n",
      "\n",
      "Iteration: 874\n",
      "RMSE: 4.52117\n",
      "\n",
      "Iteration: 875\n",
      "RMSE: 4.52593\n",
      "\n",
      "Iteration: 876\n",
      "RMSE: 4.5243\n",
      "\n",
      "Iteration: 877\n",
      "RMSE: 4.52011\n",
      "\n",
      "Iteration: 878\n",
      "RMSE: 4.52336\n",
      "\n",
      "Iteration: 879\n",
      "RMSE: 4.52029\n",
      "\n",
      "Iteration: 880\n",
      "RMSE: 4.52199\n",
      "\n",
      "Iteration: 881\n",
      "RMSE: 4.52244\n",
      "\n",
      "Iteration: 882\n",
      "RMSE: 4.5225\n",
      "\n",
      "Iteration: 883\n",
      "RMSE: 4.52427\n",
      "\n",
      "Iteration: 884\n",
      "RMSE: 4.52516\n",
      "\n",
      "Iteration: 885\n",
      "RMSE: 4.5242\n",
      "\n",
      "Iteration: 886\n",
      "RMSE: 4.52271\n",
      "\n",
      "Iteration: 887\n",
      "RMSE: 4.52822\n",
      "\n",
      "Iteration: 888\n",
      "RMSE: 4.5245\n",
      "\n",
      "Iteration: 889\n",
      "RMSE: 4.52579\n",
      "\n",
      "Iteration: 890\n",
      "RMSE: 4.52192\n",
      "\n",
      "Iteration: 891\n",
      "RMSE: 4.52051\n",
      "\n",
      "Iteration: 892\n",
      "RMSE: 4.52079\n",
      "\n",
      "Iteration: 893\n",
      "RMSE: 4.5188\n",
      "\n",
      "Iteration: 894\n",
      "RMSE: 4.51464\n",
      "\n",
      "Iteration: 895\n",
      "RMSE: 4.51549\n",
      "\n",
      "Iteration: 896\n",
      "RMSE: 4.51603\n",
      "\n",
      "Iteration: 897\n",
      "RMSE: 4.51803\n",
      "\n",
      "Iteration: 898\n",
      "RMSE: 4.51942\n",
      "\n",
      "Iteration: 899\n",
      "RMSE: 4.52185\n",
      "\n",
      "Iteration: 900\n",
      "RMSE: 4.51905\n",
      "\n",
      "Iteration: 901\n",
      "RMSE: 4.52046\n",
      "\n",
      "Iteration: 902\n",
      "RMSE: 4.51986\n",
      "\n",
      "Iteration: 903\n",
      "RMSE: 4.52328\n",
      "\n",
      "Iteration: 904\n",
      "RMSE: 4.52418\n",
      "\n",
      "Iteration: 905\n",
      "RMSE: 4.52608\n",
      "\n",
      "Iteration: 906\n",
      "RMSE: 4.52332\n",
      "\n",
      "Iteration: 907\n",
      "RMSE: 4.51948\n",
      "\n",
      "Iteration: 908\n",
      "RMSE: 4.52113\n",
      "\n",
      "Iteration: 909\n",
      "RMSE: 4.5165\n",
      "\n",
      "Iteration: 910\n",
      "RMSE: 4.5155\n",
      "\n",
      "Iteration: 911\n",
      "RMSE: 4.5213\n",
      "\n",
      "Iteration: 912\n",
      "RMSE: 4.51997\n",
      "\n",
      "Iteration: 913\n",
      "RMSE: 4.52115\n",
      "\n",
      "Iteration: 914\n",
      "RMSE: 4.51878\n",
      "\n",
      "Iteration: 915\n",
      "RMSE: 4.51856\n",
      "\n",
      "Iteration: 916\n",
      "RMSE: 4.52534\n",
      "\n",
      "Iteration: 917\n",
      "RMSE: 4.52514\n",
      "\n",
      "Iteration: 918\n",
      "RMSE: 4.52971\n",
      "\n",
      "Iteration: 919\n",
      "RMSE: 4.52668\n",
      "\n",
      "Iteration: 920\n",
      "RMSE: 4.52256\n",
      "\n",
      "Iteration: 921\n",
      "RMSE: 4.53017\n",
      "\n",
      "Iteration: 922\n",
      "RMSE: 4.52728\n",
      "\n",
      "Iteration: 923\n",
      "RMSE: 4.52537\n",
      "\n",
      "Iteration: 924\n",
      "RMSE: 4.52452\n",
      "\n",
      "Iteration: 925\n",
      "RMSE: 4.52477\n",
      "\n",
      "Iteration: 926\n",
      "RMSE: 4.52484\n",
      "\n",
      "Iteration: 927\n",
      "RMSE: 4.52344\n",
      "\n",
      "Iteration: 928\n",
      "RMSE: 4.52644\n",
      "\n",
      "Iteration: 929\n",
      "RMSE: 4.52175\n",
      "\n",
      "Iteration: 930\n",
      "RMSE: 4.52767\n",
      "\n",
      "Iteration: 931\n",
      "RMSE: 4.53032\n",
      "\n",
      "Iteration: 932\n",
      "RMSE: 4.52528\n",
      "\n",
      "Iteration: 933\n",
      "RMSE: 4.52911\n",
      "\n",
      "Iteration: 934\n",
      "RMSE: 4.52504\n",
      "\n",
      "Iteration: 935\n",
      "RMSE: 4.52358\n",
      "\n",
      "Iteration: 936\n",
      "RMSE: 4.52341\n",
      "\n",
      "Iteration: 937\n",
      "RMSE: 4.52468\n",
      "\n",
      "Iteration: 938\n",
      "RMSE: 4.52237\n",
      "\n",
      "Iteration: 939\n",
      "RMSE: 4.52759\n",
      "\n",
      "Iteration: 940\n",
      "RMSE: 4.5322\n",
      "\n",
      "Iteration: 941\n",
      "RMSE: 4.53629\n",
      "\n",
      "Iteration: 942\n",
      "RMSE: 4.53121\n",
      "\n",
      "Iteration: 943\n",
      "RMSE: 4.53599\n",
      "\n",
      "Iteration: 944\n",
      "RMSE: 4.53496\n",
      "\n",
      "Iteration: 945\n",
      "RMSE: 4.53192\n",
      "\n",
      "Iteration: 946\n",
      "RMSE: 4.53273\n",
      "\n",
      "Iteration: 947\n",
      "RMSE: 4.52694\n",
      "\n",
      "Iteration: 948\n",
      "RMSE: 4.53442\n",
      "\n",
      "Iteration: 949\n",
      "RMSE: 4.52953\n",
      "\n",
      "Iteration: 950\n",
      "RMSE: 4.52779\n",
      "\n",
      "Iteration: 951\n",
      "RMSE: 4.5288\n",
      "\n",
      "Iteration: 952\n",
      "RMSE: 4.52918\n",
      "\n",
      "Iteration: 953\n",
      "RMSE: 4.5308\n",
      "\n",
      "Iteration: 954\n",
      "RMSE: 4.5365\n",
      "\n",
      "Iteration: 955\n",
      "RMSE: 4.5374\n",
      "\n",
      "Iteration: 956\n",
      "RMSE: 4.53578\n",
      "\n",
      "Iteration: 957\n",
      "RMSE: 4.53429\n",
      "\n",
      "Iteration: 958\n",
      "RMSE: 4.53475\n",
      "\n",
      "Iteration: 959\n",
      "RMSE: 4.53505\n",
      "\n",
      "Iteration: 960\n",
      "RMSE: 4.53629\n",
      "\n",
      "Iteration: 961\n",
      "RMSE: 4.5373\n",
      "\n",
      "Iteration: 962\n",
      "RMSE: 4.53279\n",
      "\n",
      "Iteration: 963\n",
      "RMSE: 4.5353\n",
      "\n",
      "Iteration: 964\n",
      "RMSE: 4.53679\n",
      "\n",
      "Iteration: 965\n",
      "RMSE: 4.53489\n",
      "\n",
      "Iteration: 966\n",
      "RMSE: 4.53818\n",
      "\n",
      "Iteration: 967\n",
      "RMSE: 4.53242\n",
      "\n",
      "Iteration: 968\n",
      "RMSE: 4.53528\n",
      "\n",
      "Iteration: 969\n",
      "RMSE: 4.53466\n",
      "\n",
      "Iteration: 970\n",
      "RMSE: 4.52915\n",
      "\n",
      "Iteration: 971\n",
      "RMSE: 4.53365\n",
      "\n",
      "Iteration: 972\n",
      "RMSE: 4.53147\n",
      "\n",
      "Iteration: 973\n",
      "RMSE: 4.53764\n",
      "\n",
      "Iteration: 974\n",
      "RMSE: 4.53687\n",
      "\n",
      "Iteration: 975\n",
      "RMSE: 4.52839\n",
      "\n",
      "Iteration: 976\n",
      "RMSE: 4.53139\n",
      "\n",
      "Iteration: 977\n",
      "RMSE: 4.53105\n",
      "\n",
      "Iteration: 978\n",
      "RMSE: 4.53345\n",
      "\n",
      "Iteration: 979\n",
      "RMSE: 4.53612\n",
      "\n",
      "Iteration: 980\n",
      "RMSE: 4.53581\n",
      "\n",
      "Iteration: 981\n",
      "RMSE: 4.53507\n",
      "\n",
      "Iteration: 982\n",
      "RMSE: 4.53987\n",
      "\n",
      "Iteration: 983\n",
      "RMSE: 4.5382\n",
      "\n",
      "Iteration: 984\n",
      "RMSE: 4.53801\n",
      "\n",
      "Iteration: 985\n",
      "RMSE: 4.53654\n",
      "\n",
      "Iteration: 986\n",
      "RMSE: 4.53308\n",
      "\n",
      "Iteration: 987\n",
      "RMSE: 4.53264\n",
      "\n",
      "Iteration: 988\n",
      "RMSE: 4.53146\n",
      "\n",
      "Iteration: 989\n",
      "RMSE: 4.52973\n",
      "\n",
      "Iteration: 990\n",
      "RMSE: 4.53141\n",
      "\n",
      "Iteration: 991\n",
      "RMSE: 4.53123\n",
      "\n",
      "Iteration: 992\n",
      "RMSE: 4.53162\n",
      "\n",
      "Iteration: 993\n",
      "RMSE: 4.53167\n",
      "\n",
      "Iteration: 994\n",
      "RMSE: 4.53414\n",
      "\n",
      "Iteration: 995\n",
      "RMSE: 4.53266\n",
      "\n",
      "Iteration: 996\n",
      "RMSE: 4.53523\n",
      "\n",
      "Iteration: 997\n",
      "RMSE: 4.5357\n",
      "\n",
      "Iteration: 998\n",
      "RMSE: 4.53572\n",
      "\n",
      "Iteration: 999\n",
      "RMSE: 4.53471\n",
      "\n",
      "Iteration: 1000\n",
      "RMSE: 4.52807\n",
      "\n",
      "Imputation MAPE: 0.1038\n",
      "Imputation RMSE: 4.48337\n",
      "\n",
      "Running time: 3183 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 144])\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \"X\": 0.1 * np.random.rand(dim2, rank)}\n",
    "burn_iter = 1000\n",
    "gibbs_iter = 100\n",
    "BTMF(dense_mat, sparse_mat, init, rank, time_lags, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "dense_mat = pd.read_csv('../datasets/Seattle-data-set/mat.csv', index_col = 0)\n",
    "RM_mat = pd.read_csv('../datasets/Seattle-data-set/RM_mat.csv', index_col = 0)\n",
    "dense_mat = dense_mat.values\n",
    "RM_mat = RM_mat.values\n",
    "\n",
    "missing_rate = 0.4\n",
    "\n",
    "# =============================================================================\n",
    "### Random missing (RM) scenario\n",
    "### Set the RM scenario by:\n",
    "binary_mat = np.round(RM_mat + 0.5 - missing_rate)\n",
    "# =============================================================================\n",
    "\n",
    "sparse_mat = np.multiply(dense_mat, binary_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 8.54652\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 8.25793\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 6.82373\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 6.29088\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 6.26116\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 6.11663\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 5.9606\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 5.94366\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 5.90364\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 5.79692\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: 5.77708\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: 5.75393\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: 5.64862\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: 5.54195\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: 5.47609\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: 5.42693\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: 5.42135\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: 5.41639\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: 5.4097\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: 5.39612\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: 5.3333\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: 5.23819\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: 5.1996\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: 5.18862\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: 5.1844\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: 5.17956\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: 5.17783\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: 5.17189\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: 5.15882\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: 5.13258\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: 5.1249\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: 5.1116\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: 5.07737\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: 5.05637\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: 5.04501\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: 5.02225\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: 5.00356\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: 4.99315\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: 4.98749\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: 4.97924\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: 4.95565\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: 4.93692\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: 4.92391\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: 4.90078\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: 4.89054\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: 4.88453\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: 4.87351\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: 4.8561\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: 4.84395\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: 4.83496\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: 4.81409\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: 4.80029\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: 4.79179\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: 4.78074\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: 4.76313\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: 4.75216\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: 4.74665\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: 4.73792\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: 4.72666\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: 4.71382\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: 4.70261\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: 4.69827\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: 4.68863\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: 4.67631\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: 4.66682\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: 4.65463\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: 4.64508\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: 4.6337\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: 4.62508\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: 4.61585\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: 4.60905\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: 4.6052\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: 4.6026\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: 4.59571\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: 4.591\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: 4.57644\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: 4.56678\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: 4.56103\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: 4.55562\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: 4.5515\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: 4.54187\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: 4.53424\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: 4.52753\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: 4.51906\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: 4.50593\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: 4.50458\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: 4.49481\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: 4.48946\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: 4.48422\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: 4.48155\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: 4.48171\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: 4.47774\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: 4.47049\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: 4.46471\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: 4.45407\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: 4.45284\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: 4.44671\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: 4.44111\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: 4.43353\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: 4.4253\n",
      "\n",
      "Iteration: 101\n",
      "RMSE: 4.42155\n",
      "\n",
      "Iteration: 102\n",
      "RMSE: 4.41482\n",
      "\n",
      "Iteration: 103\n",
      "RMSE: 4.41102\n",
      "\n",
      "Iteration: 104\n",
      "RMSE: 4.40861\n",
      "\n",
      "Iteration: 105\n",
      "RMSE: 4.40511\n",
      "\n",
      "Iteration: 106\n",
      "RMSE: 4.404\n",
      "\n",
      "Iteration: 107\n",
      "RMSE: 4.40011\n",
      "\n",
      "Iteration: 108\n",
      "RMSE: 4.3981\n",
      "\n",
      "Iteration: 109\n",
      "RMSE: 4.39567\n",
      "\n",
      "Iteration: 110\n",
      "RMSE: 4.39007\n",
      "\n",
      "Iteration: 111\n",
      "RMSE: 4.38508\n",
      "\n",
      "Iteration: 112\n",
      "RMSE: 4.37766\n",
      "\n",
      "Iteration: 113\n",
      "RMSE: 4.36911\n",
      "\n",
      "Iteration: 114\n",
      "RMSE: 4.36386\n",
      "\n",
      "Iteration: 115\n",
      "RMSE: 4.36158\n",
      "\n",
      "Iteration: 116\n",
      "RMSE: 4.35696\n",
      "\n",
      "Iteration: 117\n",
      "RMSE: 4.35327\n",
      "\n",
      "Iteration: 118\n",
      "RMSE: 4.34679\n",
      "\n",
      "Iteration: 119\n",
      "RMSE: 4.34363\n",
      "\n",
      "Iteration: 120\n",
      "RMSE: 4.33815\n",
      "\n",
      "Iteration: 121\n",
      "RMSE: 4.33279\n",
      "\n",
      "Iteration: 122\n",
      "RMSE: 4.32862\n",
      "\n",
      "Iteration: 123\n",
      "RMSE: 4.32272\n",
      "\n",
      "Iteration: 124\n",
      "RMSE: 4.31575\n",
      "\n",
      "Iteration: 125\n",
      "RMSE: 4.3088\n",
      "\n",
      "Iteration: 126\n",
      "RMSE: 4.30296\n",
      "\n",
      "Iteration: 127\n",
      "RMSE: 4.3008\n",
      "\n",
      "Iteration: 128\n",
      "RMSE: 4.29517\n",
      "\n",
      "Iteration: 129\n",
      "RMSE: 4.2874\n",
      "\n",
      "Iteration: 130\n",
      "RMSE: 4.28702\n",
      "\n",
      "Iteration: 131\n",
      "RMSE: 4.2855\n",
      "\n",
      "Iteration: 132\n",
      "RMSE: 4.28099\n",
      "\n",
      "Iteration: 133\n",
      "RMSE: 4.2749\n",
      "\n",
      "Iteration: 134\n",
      "RMSE: 4.27634\n",
      "\n",
      "Iteration: 135\n",
      "RMSE: 4.26989\n",
      "\n",
      "Iteration: 136\n",
      "RMSE: 4.27053\n",
      "\n",
      "Iteration: 137\n",
      "RMSE: 4.2677\n",
      "\n",
      "Iteration: 138\n",
      "RMSE: 4.26524\n",
      "\n",
      "Iteration: 139\n",
      "RMSE: 4.26579\n",
      "\n",
      "Iteration: 140\n",
      "RMSE: 4.2608\n",
      "\n",
      "Iteration: 141\n",
      "RMSE: 4.26206\n",
      "\n",
      "Iteration: 142\n",
      "RMSE: 4.25638\n",
      "\n",
      "Iteration: 143\n",
      "RMSE: 4.25494\n",
      "\n",
      "Iteration: 144\n",
      "RMSE: 4.25412\n",
      "\n",
      "Iteration: 145\n",
      "RMSE: 4.25232\n",
      "\n",
      "Iteration: 146\n",
      "RMSE: 4.24726\n",
      "\n",
      "Iteration: 147\n",
      "RMSE: 4.24652\n",
      "\n",
      "Iteration: 148\n",
      "RMSE: 4.24235\n",
      "\n",
      "Iteration: 149\n",
      "RMSE: 4.23943\n",
      "\n",
      "Iteration: 150\n",
      "RMSE: 4.23586\n",
      "\n",
      "Iteration: 151\n",
      "RMSE: 4.23325\n",
      "\n",
      "Iteration: 152\n",
      "RMSE: 4.23221\n",
      "\n",
      "Iteration: 153\n",
      "RMSE: 4.2319\n",
      "\n",
      "Iteration: 154\n",
      "RMSE: 4.22713\n",
      "\n",
      "Iteration: 155\n",
      "RMSE: 4.22729\n",
      "\n",
      "Iteration: 156\n",
      "RMSE: 4.22323\n",
      "\n",
      "Iteration: 157\n",
      "RMSE: 4.21992\n",
      "\n",
      "Iteration: 158\n",
      "RMSE: 4.21569\n",
      "\n",
      "Iteration: 159\n",
      "RMSE: 4.21745\n",
      "\n",
      "Iteration: 160\n",
      "RMSE: 4.21479\n",
      "\n",
      "Iteration: 161\n",
      "RMSE: 4.20791\n",
      "\n",
      "Iteration: 162\n",
      "RMSE: 4.20365\n",
      "\n",
      "Iteration: 163\n",
      "RMSE: 4.20512\n",
      "\n",
      "Iteration: 164\n",
      "RMSE: 4.20221\n",
      "\n",
      "Iteration: 165\n",
      "RMSE: 4.19775\n",
      "\n",
      "Iteration: 166\n",
      "RMSE: 4.19964\n",
      "\n",
      "Iteration: 167\n",
      "RMSE: 4.19683\n",
      "\n",
      "Iteration: 168\n",
      "RMSE: 4.19127\n",
      "\n",
      "Iteration: 169\n",
      "RMSE: 4.18714\n",
      "\n",
      "Iteration: 170\n",
      "RMSE: 4.18431\n",
      "\n",
      "Iteration: 171\n",
      "RMSE: 4.18175\n",
      "\n",
      "Iteration: 172\n",
      "RMSE: 4.18249\n",
      "\n",
      "Iteration: 173\n",
      "RMSE: 4.18414\n",
      "\n",
      "Iteration: 174\n",
      "RMSE: 4.18181\n",
      "\n",
      "Iteration: 175\n",
      "RMSE: 4.18072\n",
      "\n",
      "Iteration: 176\n",
      "RMSE: 4.17982\n",
      "\n",
      "Iteration: 177\n",
      "RMSE: 4.17537\n",
      "\n",
      "Iteration: 178\n",
      "RMSE: 4.17699\n",
      "\n",
      "Iteration: 179\n",
      "RMSE: 4.17467\n",
      "\n",
      "Iteration: 180\n",
      "RMSE: 4.17091\n",
      "\n",
      "Iteration: 181\n",
      "RMSE: 4.16651\n",
      "\n",
      "Iteration: 182\n",
      "RMSE: 4.16448\n",
      "\n",
      "Iteration: 183\n",
      "RMSE: 4.16531\n",
      "\n",
      "Iteration: 184\n",
      "RMSE: 4.16307\n",
      "\n",
      "Iteration: 185\n",
      "RMSE: 4.16212\n",
      "\n",
      "Iteration: 186\n",
      "RMSE: 4.16161\n",
      "\n",
      "Iteration: 187\n",
      "RMSE: 4.16432\n",
      "\n",
      "Iteration: 188\n",
      "RMSE: 4.1601\n",
      "\n",
      "Iteration: 189\n",
      "RMSE: 4.15846\n",
      "\n",
      "Iteration: 190\n",
      "RMSE: 4.15702\n",
      "\n",
      "Iteration: 191\n",
      "RMSE: 4.15735\n",
      "\n",
      "Iteration: 192\n",
      "RMSE: 4.15521\n",
      "\n",
      "Iteration: 193\n",
      "RMSE: 4.15507\n",
      "\n",
      "Iteration: 194\n",
      "RMSE: 4.15309\n",
      "\n",
      "Iteration: 195\n",
      "RMSE: 4.15236\n",
      "\n",
      "Iteration: 196\n",
      "RMSE: 4.15341\n",
      "\n",
      "Iteration: 197\n",
      "RMSE: 4.15087\n",
      "\n",
      "Iteration: 198\n",
      "RMSE: 4.14996\n",
      "\n",
      "Iteration: 199\n",
      "RMSE: 4.14509\n",
      "\n",
      "Iteration: 200\n",
      "RMSE: 4.14444\n",
      "\n",
      "Iteration: 201\n",
      "RMSE: 4.14199\n",
      "\n",
      "Iteration: 202\n",
      "RMSE: 4.14101\n",
      "\n",
      "Iteration: 203\n",
      "RMSE: 4.13956\n",
      "\n",
      "Iteration: 204\n",
      "RMSE: 4.14083\n",
      "\n",
      "Iteration: 205\n",
      "RMSE: 4.13747\n",
      "\n",
      "Iteration: 206\n",
      "RMSE: 4.13314\n",
      "\n",
      "Iteration: 207\n",
      "RMSE: 4.13328\n",
      "\n",
      "Iteration: 208\n",
      "RMSE: 4.13084\n",
      "\n",
      "Iteration: 209\n",
      "RMSE: 4.12983\n",
      "\n",
      "Iteration: 210\n",
      "RMSE: 4.13019\n",
      "\n",
      "Iteration: 211\n",
      "RMSE: 4.12653\n",
      "\n",
      "Iteration: 212\n",
      "RMSE: 4.12689\n",
      "\n",
      "Iteration: 213\n",
      "RMSE: 4.12694\n",
      "\n",
      "Iteration: 214\n",
      "RMSE: 4.12879\n",
      "\n",
      "Iteration: 215\n",
      "RMSE: 4.12763\n",
      "\n",
      "Iteration: 216\n",
      "RMSE: 4.12503\n",
      "\n",
      "Iteration: 217\n",
      "RMSE: 4.12357\n",
      "\n",
      "Iteration: 218\n",
      "RMSE: 4.12456\n",
      "\n",
      "Iteration: 219\n",
      "RMSE: 4.12417\n",
      "\n",
      "Iteration: 220\n",
      "RMSE: 4.11768\n",
      "\n",
      "Iteration: 221\n",
      "RMSE: 4.11751\n",
      "\n",
      "Iteration: 222\n",
      "RMSE: 4.11685\n",
      "\n",
      "Iteration: 223\n",
      "RMSE: 4.11519\n",
      "\n",
      "Iteration: 224\n",
      "RMSE: 4.1137\n",
      "\n",
      "Iteration: 225\n",
      "RMSE: 4.11519\n",
      "\n",
      "Iteration: 226\n",
      "RMSE: 4.11511\n",
      "\n",
      "Iteration: 227\n",
      "RMSE: 4.11472\n",
      "\n",
      "Iteration: 228\n",
      "RMSE: 4.10936\n",
      "\n",
      "Iteration: 229\n",
      "RMSE: 4.10771\n",
      "\n",
      "Iteration: 230\n",
      "RMSE: 4.10801\n",
      "\n",
      "Iteration: 231\n",
      "RMSE: 4.10893\n",
      "\n",
      "Iteration: 232\n",
      "RMSE: 4.10763\n",
      "\n",
      "Iteration: 233\n",
      "RMSE: 4.10631\n",
      "\n",
      "Iteration: 234\n",
      "RMSE: 4.10464\n",
      "\n",
      "Iteration: 235\n",
      "RMSE: 4.10312\n",
      "\n",
      "Iteration: 236\n",
      "RMSE: 4.10098\n",
      "\n",
      "Iteration: 237\n",
      "RMSE: 4.1029\n",
      "\n",
      "Iteration: 238\n",
      "RMSE: 4.10243\n",
      "\n",
      "Iteration: 239\n",
      "RMSE: 4.10198\n",
      "\n",
      "Iteration: 240\n",
      "RMSE: 4.10195\n",
      "\n",
      "Iteration: 241\n",
      "RMSE: 4.10301\n",
      "\n",
      "Iteration: 242\n",
      "RMSE: 4.1047\n",
      "\n",
      "Iteration: 243\n",
      "RMSE: 4.09984\n",
      "\n",
      "Iteration: 244\n",
      "RMSE: 4.10114\n",
      "\n",
      "Iteration: 245\n",
      "RMSE: 4.10002\n",
      "\n",
      "Iteration: 246\n",
      "RMSE: 4.09717\n",
      "\n",
      "Iteration: 247\n",
      "RMSE: 4.09676\n",
      "\n",
      "Iteration: 248\n",
      "RMSE: 4.09634\n",
      "\n",
      "Iteration: 249\n",
      "RMSE: 4.09156\n",
      "\n",
      "Iteration: 250\n",
      "RMSE: 4.08978\n",
      "\n",
      "Iteration: 251\n",
      "RMSE: 4.09043\n",
      "\n",
      "Iteration: 252\n",
      "RMSE: 4.09203\n",
      "\n",
      "Iteration: 253\n",
      "RMSE: 4.089\n",
      "\n",
      "Iteration: 254\n",
      "RMSE: 4.08641\n",
      "\n",
      "Iteration: 255\n",
      "RMSE: 4.08697\n",
      "\n",
      "Iteration: 256\n",
      "RMSE: 4.08632\n",
      "\n",
      "Iteration: 257\n",
      "RMSE: 4.08768\n",
      "\n",
      "Iteration: 258\n",
      "RMSE: 4.08203\n",
      "\n",
      "Iteration: 259\n",
      "RMSE: 4.08772\n",
      "\n",
      "Iteration: 260\n",
      "RMSE: 4.08117\n",
      "\n",
      "Iteration: 261\n",
      "RMSE: 4.07978\n",
      "\n",
      "Iteration: 262\n",
      "RMSE: 4.079\n",
      "\n",
      "Iteration: 263\n",
      "RMSE: 4.07859\n",
      "\n",
      "Iteration: 264\n",
      "RMSE: 4.07441\n",
      "\n",
      "Iteration: 265\n",
      "RMSE: 4.07062\n",
      "\n",
      "Iteration: 266\n",
      "RMSE: 4.07282\n",
      "\n",
      "Iteration: 267\n",
      "RMSE: 4.06806\n",
      "\n",
      "Iteration: 268\n",
      "RMSE: 4.06788\n",
      "\n",
      "Iteration: 269\n",
      "RMSE: 4.07162\n",
      "\n",
      "Iteration: 270\n",
      "RMSE: 4.06768\n",
      "\n",
      "Iteration: 271\n",
      "RMSE: 4.06571\n",
      "\n",
      "Iteration: 272\n",
      "RMSE: 4.06529\n",
      "\n",
      "Iteration: 273\n",
      "RMSE: 4.06396\n",
      "\n",
      "Iteration: 274\n",
      "RMSE: 4.06522\n",
      "\n",
      "Iteration: 275\n",
      "RMSE: 4.06222\n",
      "\n",
      "Iteration: 276\n",
      "RMSE: 4.06297\n",
      "\n",
      "Iteration: 277\n",
      "RMSE: 4.06467\n",
      "\n",
      "Iteration: 278\n",
      "RMSE: 4.06722\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 279\n",
      "RMSE: 4.0684\n",
      "\n",
      "Iteration: 280\n",
      "RMSE: 4.06494\n",
      "\n",
      "Iteration: 281\n",
      "RMSE: 4.06389\n",
      "\n",
      "Iteration: 282\n",
      "RMSE: 4.06309\n",
      "\n",
      "Iteration: 283\n",
      "RMSE: 4.06212\n",
      "\n",
      "Iteration: 284\n",
      "RMSE: 4.06207\n",
      "\n",
      "Iteration: 285\n",
      "RMSE: 4.05934\n",
      "\n",
      "Iteration: 286\n",
      "RMSE: 4.0612\n",
      "\n",
      "Iteration: 287\n",
      "RMSE: 4.05956\n",
      "\n",
      "Iteration: 288\n",
      "RMSE: 4.05898\n",
      "\n",
      "Iteration: 289\n",
      "RMSE: 4.06115\n",
      "\n",
      "Iteration: 290\n",
      "RMSE: 4.06128\n",
      "\n",
      "Iteration: 291\n",
      "RMSE: 4.0611\n",
      "\n",
      "Iteration: 292\n",
      "RMSE: 4.0583\n",
      "\n",
      "Iteration: 293\n",
      "RMSE: 4.06172\n",
      "\n",
      "Iteration: 294\n",
      "RMSE: 4.06312\n",
      "\n",
      "Iteration: 295\n",
      "RMSE: 4.06149\n",
      "\n",
      "Iteration: 296\n",
      "RMSE: 4.06089\n",
      "\n",
      "Iteration: 297\n",
      "RMSE: 4.0614\n",
      "\n",
      "Iteration: 298\n",
      "RMSE: 4.06076\n",
      "\n",
      "Iteration: 299\n",
      "RMSE: 4.05725\n",
      "\n",
      "Iteration: 300\n",
      "RMSE: 4.05363\n",
      "\n",
      "Iteration: 301\n",
      "RMSE: 4.05756\n",
      "\n",
      "Iteration: 302\n",
      "RMSE: 4.05997\n",
      "\n",
      "Iteration: 303\n",
      "RMSE: 4.05964\n",
      "\n",
      "Iteration: 304\n",
      "RMSE: 4.05655\n",
      "\n",
      "Iteration: 305\n",
      "RMSE: 4.05586\n",
      "\n",
      "Iteration: 306\n",
      "RMSE: 4.05818\n",
      "\n",
      "Iteration: 307\n",
      "RMSE: 4.05871\n",
      "\n",
      "Iteration: 308\n",
      "RMSE: 4.05555\n",
      "\n",
      "Iteration: 309\n",
      "RMSE: 4.05488\n",
      "\n",
      "Iteration: 310\n",
      "RMSE: 4.05449\n",
      "\n",
      "Iteration: 311\n",
      "RMSE: 4.05731\n",
      "\n",
      "Iteration: 312\n",
      "RMSE: 4.05424\n",
      "\n",
      "Iteration: 313\n",
      "RMSE: 4.05726\n",
      "\n",
      "Iteration: 314\n",
      "RMSE: 4.05514\n",
      "\n",
      "Iteration: 315\n",
      "RMSE: 4.05924\n",
      "\n",
      "Iteration: 316\n",
      "RMSE: 4.05616\n",
      "\n",
      "Iteration: 317\n",
      "RMSE: 4.05903\n",
      "\n",
      "Iteration: 318\n",
      "RMSE: 4.05738\n",
      "\n",
      "Iteration: 319\n",
      "RMSE: 4.05665\n",
      "\n",
      "Iteration: 320\n",
      "RMSE: 4.05438\n",
      "\n",
      "Iteration: 321\n",
      "RMSE: 4.05673\n",
      "\n",
      "Iteration: 322\n",
      "RMSE: 4.05717\n",
      "\n",
      "Iteration: 323\n",
      "RMSE: 4.05317\n",
      "\n",
      "Iteration: 324\n",
      "RMSE: 4.05329\n",
      "\n",
      "Iteration: 325\n",
      "RMSE: 4.05718\n",
      "\n",
      "Iteration: 326\n",
      "RMSE: 4.05526\n",
      "\n",
      "Iteration: 327\n",
      "RMSE: 4.0578\n",
      "\n",
      "Iteration: 328\n",
      "RMSE: 4.056\n",
      "\n",
      "Iteration: 329\n",
      "RMSE: 4.05501\n",
      "\n",
      "Iteration: 330\n",
      "RMSE: 4.05156\n",
      "\n",
      "Iteration: 331\n",
      "RMSE: 4.05288\n",
      "\n",
      "Iteration: 332\n",
      "RMSE: 4.05339\n",
      "\n",
      "Iteration: 333\n",
      "RMSE: 4.05627\n",
      "\n",
      "Iteration: 334\n",
      "RMSE: 4.05635\n",
      "\n",
      "Iteration: 335\n",
      "RMSE: 4.0532\n",
      "\n",
      "Iteration: 336\n",
      "RMSE: 4.05467\n",
      "\n",
      "Iteration: 337\n",
      "RMSE: 4.04918\n",
      "\n",
      "Iteration: 338\n",
      "RMSE: 4.05194\n",
      "\n",
      "Iteration: 339\n",
      "RMSE: 4.0515\n",
      "\n",
      "Iteration: 340\n",
      "RMSE: 4.05112\n",
      "\n",
      "Iteration: 341\n",
      "RMSE: 4.05337\n",
      "\n",
      "Iteration: 342\n",
      "RMSE: 4.04989\n",
      "\n",
      "Iteration: 343\n",
      "RMSE: 4.04625\n",
      "\n",
      "Iteration: 344\n",
      "RMSE: 4.04658\n",
      "\n",
      "Iteration: 345\n",
      "RMSE: 4.04929\n",
      "\n",
      "Iteration: 346\n",
      "RMSE: 4.04718\n",
      "\n",
      "Iteration: 347\n",
      "RMSE: 4.04987\n",
      "\n",
      "Iteration: 348\n",
      "RMSE: 4.04604\n",
      "\n",
      "Iteration: 349\n",
      "RMSE: 4.0463\n",
      "\n",
      "Iteration: 350\n",
      "RMSE: 4.04668\n",
      "\n",
      "Iteration: 351\n",
      "RMSE: 4.04816\n",
      "\n",
      "Iteration: 352\n",
      "RMSE: 4.04784\n",
      "\n",
      "Iteration: 353\n",
      "RMSE: 4.04726\n",
      "\n",
      "Iteration: 354\n",
      "RMSE: 4.05267\n",
      "\n",
      "Iteration: 355\n",
      "RMSE: 4.04674\n",
      "\n",
      "Iteration: 356\n",
      "RMSE: 4.0483\n",
      "\n",
      "Iteration: 357\n",
      "RMSE: 4.04685\n",
      "\n",
      "Iteration: 358\n",
      "RMSE: 4.05342\n",
      "\n",
      "Iteration: 359\n",
      "RMSE: 4.04822\n",
      "\n",
      "Iteration: 360\n",
      "RMSE: 4.052\n",
      "\n",
      "Iteration: 361\n",
      "RMSE: 4.05\n",
      "\n",
      "Iteration: 362\n",
      "RMSE: 4.05073\n",
      "\n",
      "Iteration: 363\n",
      "RMSE: 4.04697\n",
      "\n",
      "Iteration: 364\n",
      "RMSE: 4.04859\n",
      "\n",
      "Iteration: 365\n",
      "RMSE: 4.04631\n",
      "\n",
      "Iteration: 366\n",
      "RMSE: 4.04836\n",
      "\n",
      "Iteration: 367\n",
      "RMSE: 4.0456\n",
      "\n",
      "Iteration: 368\n",
      "RMSE: 4.04656\n",
      "\n",
      "Iteration: 369\n",
      "RMSE: 4.04852\n",
      "\n",
      "Iteration: 370\n",
      "RMSE: 4.04559\n",
      "\n",
      "Iteration: 371\n",
      "RMSE: 4.04951\n",
      "\n",
      "Iteration: 372\n",
      "RMSE: 4.0491\n",
      "\n",
      "Iteration: 373\n",
      "RMSE: 4.04814\n",
      "\n",
      "Iteration: 374\n",
      "RMSE: 4.04593\n",
      "\n",
      "Iteration: 375\n",
      "RMSE: 4.04409\n",
      "\n",
      "Iteration: 376\n",
      "RMSE: 4.04361\n",
      "\n",
      "Iteration: 377\n",
      "RMSE: 4.04476\n",
      "\n",
      "Iteration: 378\n",
      "RMSE: 4.04576\n",
      "\n",
      "Iteration: 379\n",
      "RMSE: 4.04426\n",
      "\n",
      "Iteration: 380\n",
      "RMSE: 4.04428\n",
      "\n",
      "Iteration: 381\n",
      "RMSE: 4.0454\n",
      "\n",
      "Iteration: 382\n",
      "RMSE: 4.04438\n",
      "\n",
      "Iteration: 383\n",
      "RMSE: 4.04599\n",
      "\n",
      "Iteration: 384\n",
      "RMSE: 4.04047\n",
      "\n",
      "Iteration: 385\n",
      "RMSE: 4.04162\n",
      "\n",
      "Iteration: 386\n",
      "RMSE: 4.04225\n",
      "\n",
      "Iteration: 387\n",
      "RMSE: 4.04026\n",
      "\n",
      "Iteration: 388\n",
      "RMSE: 4.04254\n",
      "\n",
      "Iteration: 389\n",
      "RMSE: 4.04044\n",
      "\n",
      "Iteration: 390\n",
      "RMSE: 4.04225\n",
      "\n",
      "Iteration: 391\n",
      "RMSE: 4.0389\n",
      "\n",
      "Iteration: 392\n",
      "RMSE: 4.03768\n",
      "\n",
      "Iteration: 393\n",
      "RMSE: 4.04319\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/xinyuchen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:36: RuntimeWarning: covariance is not positive-semidefinite.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 394\n",
      "RMSE: 4.04085\n",
      "\n",
      "Iteration: 395\n",
      "RMSE: 4.04268\n",
      "\n",
      "Iteration: 396\n",
      "RMSE: 4.0425\n",
      "\n",
      "Iteration: 397\n",
      "RMSE: 4.04042\n",
      "\n",
      "Iteration: 398\n",
      "RMSE: 4.04092\n",
      "\n",
      "Iteration: 399\n",
      "RMSE: 4.03779\n",
      "\n",
      "Iteration: 400\n",
      "RMSE: 4.04163\n",
      "\n",
      "Iteration: 401\n",
      "RMSE: 4.04327\n",
      "\n",
      "Iteration: 402\n",
      "RMSE: 4.0422\n",
      "\n",
      "Iteration: 403\n",
      "RMSE: 4.04504\n",
      "\n",
      "Iteration: 404\n",
      "RMSE: 4.04549\n",
      "\n",
      "Iteration: 405\n",
      "RMSE: 4.04062\n",
      "\n",
      "Iteration: 406\n",
      "RMSE: 4.03777\n",
      "\n",
      "Iteration: 407\n",
      "RMSE: 4.04032\n",
      "\n",
      "Iteration: 408\n",
      "RMSE: 4.03954\n",
      "\n",
      "Iteration: 409\n",
      "RMSE: 4.04377\n",
      "\n",
      "Iteration: 410\n",
      "RMSE: 4.04143\n",
      "\n",
      "Iteration: 411\n",
      "RMSE: 4.03972\n",
      "\n",
      "Iteration: 412\n",
      "RMSE: 4.04493\n",
      "\n",
      "Iteration: 413\n",
      "RMSE: 4.04041\n",
      "\n",
      "Iteration: 414\n",
      "RMSE: 4.03843\n",
      "\n",
      "Iteration: 415\n",
      "RMSE: 4.03943\n",
      "\n",
      "Iteration: 416\n",
      "RMSE: 4.04237\n",
      "\n",
      "Iteration: 417\n",
      "RMSE: 4.03858\n",
      "\n",
      "Iteration: 418\n",
      "RMSE: 4.03928\n",
      "\n",
      "Iteration: 419\n",
      "RMSE: 4.04381\n",
      "\n",
      "Iteration: 420\n",
      "RMSE: 4.04177\n",
      "\n",
      "Iteration: 421\n",
      "RMSE: 4.03933\n",
      "\n",
      "Iteration: 422\n",
      "RMSE: 4.04199\n",
      "\n",
      "Iteration: 423\n",
      "RMSE: 4.03973\n",
      "\n",
      "Iteration: 424\n",
      "RMSE: 4.04423\n",
      "\n",
      "Iteration: 425\n",
      "RMSE: 4.03968\n",
      "\n",
      "Iteration: 426\n",
      "RMSE: 4.04267\n",
      "\n",
      "Iteration: 427\n",
      "RMSE: 4.04012\n",
      "\n",
      "Iteration: 428\n",
      "RMSE: 4.04209\n",
      "\n",
      "Iteration: 429\n",
      "RMSE: 4.03841\n",
      "\n",
      "Iteration: 430\n",
      "RMSE: 4.03882\n",
      "\n",
      "Iteration: 431\n",
      "RMSE: 4.03768\n",
      "\n",
      "Iteration: 432\n",
      "RMSE: 4.03913\n",
      "\n",
      "Iteration: 433\n",
      "RMSE: 4.03646\n",
      "\n",
      "Iteration: 434\n",
      "RMSE: 4.03684\n",
      "\n",
      "Iteration: 435\n",
      "RMSE: 4.03735\n",
      "\n",
      "Iteration: 436\n",
      "RMSE: 4.03643\n",
      "\n",
      "Iteration: 437\n",
      "RMSE: 4.03717\n",
      "\n",
      "Iteration: 438\n",
      "RMSE: 4.0339\n",
      "\n",
      "Iteration: 439\n",
      "RMSE: 4.03792\n",
      "\n",
      "Iteration: 440\n",
      "RMSE: 4.03692\n",
      "\n",
      "Iteration: 441\n",
      "RMSE: 4.03944\n",
      "\n",
      "Iteration: 442\n",
      "RMSE: 4.04036\n",
      "\n",
      "Iteration: 443\n",
      "RMSE: 4.03861\n",
      "\n",
      "Iteration: 444\n",
      "RMSE: 4.04091\n",
      "\n",
      "Iteration: 445\n",
      "RMSE: 4.03963\n",
      "\n",
      "Iteration: 446\n",
      "RMSE: 4.03945\n",
      "\n",
      "Iteration: 447\n",
      "RMSE: 4.03578\n",
      "\n",
      "Iteration: 448\n",
      "RMSE: 4.03652\n",
      "\n",
      "Iteration: 449\n",
      "RMSE: 4.03756\n",
      "\n",
      "Iteration: 450\n",
      "RMSE: 4.03959\n",
      "\n",
      "Iteration: 451\n",
      "RMSE: 4.03729\n",
      "\n",
      "Iteration: 452\n",
      "RMSE: 4.03663\n",
      "\n",
      "Iteration: 453\n",
      "RMSE: 4.03817\n",
      "\n",
      "Iteration: 454\n",
      "RMSE: 4.04068\n",
      "\n",
      "Iteration: 455\n",
      "RMSE: 4.03919\n",
      "\n",
      "Iteration: 456\n",
      "RMSE: 4.03745\n",
      "\n",
      "Iteration: 457\n",
      "RMSE: 4.03931\n",
      "\n",
      "Iteration: 458\n",
      "RMSE: 4.03754\n",
      "\n",
      "Iteration: 459\n",
      "RMSE: 4.03848\n",
      "\n",
      "Iteration: 460\n",
      "RMSE: 4.03944\n",
      "\n",
      "Iteration: 461\n",
      "RMSE: 4.03829\n",
      "\n",
      "Iteration: 462\n",
      "RMSE: 4.04299\n",
      "\n",
      "Iteration: 463\n",
      "RMSE: 4.04083\n",
      "\n",
      "Iteration: 464\n",
      "RMSE: 4.03713\n",
      "\n",
      "Iteration: 465\n",
      "RMSE: 4.04204\n",
      "\n",
      "Iteration: 466\n",
      "RMSE: 4.03924\n",
      "\n",
      "Iteration: 467\n",
      "RMSE: 4.03674\n",
      "\n",
      "Iteration: 468\n",
      "RMSE: 4.04121\n",
      "\n",
      "Iteration: 469\n",
      "RMSE: 4.03888\n",
      "\n",
      "Iteration: 470\n",
      "RMSE: 4.03983\n",
      "\n",
      "Iteration: 471\n",
      "RMSE: 4.03776\n",
      "\n",
      "Iteration: 472\n",
      "RMSE: 4.04071\n",
      "\n",
      "Iteration: 473\n",
      "RMSE: 4.04284\n",
      "\n",
      "Iteration: 474\n",
      "RMSE: 4.04519\n",
      "\n",
      "Iteration: 475\n",
      "RMSE: 4.04089\n",
      "\n",
      "Iteration: 476\n",
      "RMSE: 4.04054\n",
      "\n",
      "Iteration: 477\n",
      "RMSE: 4.04145\n",
      "\n",
      "Iteration: 478\n",
      "RMSE: 4.03787\n",
      "\n",
      "Iteration: 479\n",
      "RMSE: 4.03813\n",
      "\n",
      "Iteration: 480\n",
      "RMSE: 4.03692\n",
      "\n",
      "Iteration: 481\n",
      "RMSE: 4.04137\n",
      "\n",
      "Iteration: 482\n",
      "RMSE: 4.04116\n",
      "\n",
      "Iteration: 483\n",
      "RMSE: 4.04081\n",
      "\n",
      "Iteration: 484\n",
      "RMSE: 4.03968\n",
      "\n",
      "Iteration: 485\n",
      "RMSE: 4.04026\n",
      "\n",
      "Iteration: 486\n",
      "RMSE: 4.03936\n",
      "\n",
      "Iteration: 487\n",
      "RMSE: 4.03797\n",
      "\n",
      "Iteration: 488\n",
      "RMSE: 4.03718\n",
      "\n",
      "Iteration: 489\n",
      "RMSE: 4.03592\n",
      "\n",
      "Iteration: 490\n",
      "RMSE: 4.03771\n",
      "\n",
      "Iteration: 491\n",
      "RMSE: 4.03816\n",
      "\n",
      "Iteration: 492\n",
      "RMSE: 4.03782\n",
      "\n",
      "Iteration: 493\n",
      "RMSE: 4.04069\n",
      "\n",
      "Iteration: 494\n",
      "RMSE: 4.03547\n",
      "\n",
      "Iteration: 495\n",
      "RMSE: 4.03349\n",
      "\n",
      "Iteration: 496\n",
      "RMSE: 4.03648\n",
      "\n",
      "Iteration: 497\n",
      "RMSE: 4.03858\n",
      "\n",
      "Iteration: 498\n",
      "RMSE: 4.04057\n",
      "\n",
      "Iteration: 499\n",
      "RMSE: 4.0378\n",
      "\n",
      "Iteration: 500\n",
      "RMSE: 4.03612\n",
      "\n",
      "Iteration: 501\n",
      "RMSE: 4.03503\n",
      "\n",
      "Iteration: 502\n",
      "RMSE: 4.03914\n",
      "\n",
      "Iteration: 503\n",
      "RMSE: 4.03587\n",
      "\n",
      "Iteration: 504\n",
      "RMSE: 4.0408\n",
      "\n",
      "Iteration: 505\n",
      "RMSE: 4.03868\n",
      "\n",
      "Iteration: 506\n",
      "RMSE: 4.0414\n",
      "\n",
      "Iteration: 507\n",
      "RMSE: 4.03875\n",
      "\n",
      "Iteration: 508\n",
      "RMSE: 4.03701\n",
      "\n",
      "Iteration: 509\n",
      "RMSE: 4.03803\n",
      "\n",
      "Iteration: 510\n",
      "RMSE: 4.03576\n",
      "\n",
      "Iteration: 511\n",
      "RMSE: 4.03345\n",
      "\n",
      "Iteration: 512\n",
      "RMSE: 4.03612\n",
      "\n",
      "Iteration: 513\n",
      "RMSE: 4.03484\n",
      "\n",
      "Iteration: 514\n",
      "RMSE: 4.03819\n",
      "\n",
      "Iteration: 515\n",
      "RMSE: 4.03638\n",
      "\n",
      "Iteration: 516\n",
      "RMSE: 4.0353\n",
      "\n",
      "Iteration: 517\n",
      "RMSE: 4.02947\n",
      "\n",
      "Iteration: 518\n",
      "RMSE: 4.03592\n",
      "\n",
      "Iteration: 519\n",
      "RMSE: 4.03538\n",
      "\n",
      "Iteration: 520\n",
      "RMSE: 4.0368\n",
      "\n",
      "Iteration: 521\n",
      "RMSE: 4.03988\n",
      "\n",
      "Iteration: 522\n",
      "RMSE: 4.03965\n",
      "\n",
      "Iteration: 523\n",
      "RMSE: 4.03842\n",
      "\n",
      "Iteration: 524\n",
      "RMSE: 4.03902\n",
      "\n",
      "Iteration: 525\n",
      "RMSE: 4.03709\n",
      "\n",
      "Iteration: 526\n",
      "RMSE: 4.03664\n",
      "\n",
      "Iteration: 527\n",
      "RMSE: 4.03763\n",
      "\n",
      "Iteration: 528\n",
      "RMSE: 4.03425\n",
      "\n",
      "Iteration: 529\n",
      "RMSE: 4.03415\n",
      "\n",
      "Iteration: 530\n",
      "RMSE: 4.03088\n",
      "\n",
      "Iteration: 531\n",
      "RMSE: 4.03479\n",
      "\n",
      "Iteration: 532\n",
      "RMSE: 4.03137\n",
      "\n",
      "Iteration: 533\n",
      "RMSE: 4.03254\n",
      "\n",
      "Iteration: 534\n",
      "RMSE: 4.0328\n",
      "\n",
      "Iteration: 535\n",
      "RMSE: 4.03436\n",
      "\n",
      "Iteration: 536\n",
      "RMSE: 4.03596\n",
      "\n",
      "Iteration: 537\n",
      "RMSE: 4.03814\n",
      "\n",
      "Iteration: 538\n",
      "RMSE: 4.03757\n",
      "\n",
      "Iteration: 539\n",
      "RMSE: 4.02783\n",
      "\n",
      "Iteration: 540\n",
      "RMSE: 4.03086\n",
      "\n",
      "Iteration: 541\n",
      "RMSE: 4.03276\n",
      "\n",
      "Iteration: 542\n",
      "RMSE: 4.03118\n",
      "\n",
      "Iteration: 543\n",
      "RMSE: 4.0297\n",
      "\n",
      "Iteration: 544\n",
      "RMSE: 4.03001\n",
      "\n",
      "Iteration: 545\n",
      "RMSE: 4.03049\n",
      "\n",
      "Iteration: 546\n",
      "RMSE: 4.03344\n",
      "\n"
     ]
    },
    {
     "ename": "LinAlgError",
     "evalue": "Matrix is not positive definite",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-14-e8a1e93d5c2a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mmaxiter1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mmaxiter2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mBTMF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdense_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msparse_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrank\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime_lags\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmaxiter1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmaxiter2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Running time: %d seconds'\u001b[0m\u001b[0;34m%\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mend\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-5642926d9e75>\u001b[0m in \u001b[0;36mBTMF\u001b[0;34m(dense_mat, sparse_mat, init, rank, time_lags, maxiter1, maxiter2)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mit\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmaxiter1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0mW\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample_factor_w\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mW\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSigma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample_var_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime_lags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample_factor_x\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_mat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime_lags\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mW\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSigma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0mmat_hat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-2-4ff3cab6f23d>\u001b[0m in \u001b[0;36msample_var_coefficient\u001b[0;34m(X, time_lags)\u001b[0m\n\u001b[1;32m     31\u001b[0m     \u001b[0mvar_S\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meye\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ_mat\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mZ_mat\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar_M\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar_Psi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar_M\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     32\u001b[0m     \u001b[0mSigma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minvwishart\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrank\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mdim2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime_lags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscale\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvar_S\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 33\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mmat2ten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmnrnd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar_M\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar_Psi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSigma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrank\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSigma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-2-4ff3cab6f23d>\u001b[0m in \u001b[0;36mmnrnd\u001b[0;34m(M, U, V)\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0mdim1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mM\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m     \u001b[0mX0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdim1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0mP\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcholesky\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mU\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m     \u001b[0mQ\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcholesky\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mV\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mM\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36mcholesky\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m    612\u001b[0m     \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_commonType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    613\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'D->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 614\u001b[0;31m     \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    615\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    616\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_nonposdef\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m     90\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     91\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 92\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Matrix is not positive definite\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     93\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     94\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_eigenvalues_nonconvergence\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Matrix is not positive definite"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 50\n",
    "time_lags = np.array([1, 2, 288])\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \"X\": 0.1 * np.random.rand(dim2, rank)}\n",
    "maxiter1 = 1100\n",
    "maxiter2 = 100\n",
    "BTMF(dense_mat, sparse_mat, init, rank, time_lags, maxiter1, maxiter2)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7 Multivariate Time Series Prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BTMF_burn(dense_mat, sparse_mat, init, time_lags, burn_iter):\n",
    "    \n",
    "    W = init[\"W\"]\n",
    "    X = init[\"X\"]\n",
    "    dim1, dim2 = sparse_mat.shape\n",
    "    d = time_lags.shape[0]\n",
    "    pos = np.where((dense_mat != 0) & (sparse_mat == 0))\n",
    "    position = np.where(sparse_mat != 0)\n",
    "    binary_mat = np.zeros((dim1, dim2))\n",
    "    binary_mat[position] = 1\n",
    "    tau = 1\n",
    "    for it in range(burn_iter):\n",
    "        W = sample_factor_w(sparse_mat, binary_mat, W, X, tau)\n",
    "        A, Sigma = sample_var_coefficient(X, time_lags)\n",
    "        X = sample_factor_x(sparse_mat, binary_mat, time_lags, W, X, tau, A, inv(Sigma))\n",
    "        mat_hat = np.matmul(W, X.T)\n",
    "        tau = sample_precision_tau(sparse_mat, mat_hat, position)\n",
    "        rmse = np.sqrt(np.sum((dense_mat[pos] - mat_hat[pos]) ** 2) / dense_mat[pos].shape[0])\n",
    "        if (it + 1) % 1 == 0 and it < burn_iter:\n",
    "            print('Iteration: {}'.format(it + 1))\n",
    "            print('RMSE: {:.6}'.format(rmse))\n",
    "            print()\n",
    "    return W, X, tau, A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BTMF_4cast(mat, binary_mat, num_step, time_lags, init, gibbs_iter):\n",
    "    \"\"\"Forecast (`4cast`) time series with Bayesian Temporal Matrix Factorization (BTMF).\"\"\"\n",
    "    \n",
    "    W = init[\"W\"]\n",
    "    X = init[\"X\"]\n",
    "    tau = init[\"tau\"]\n",
    "    A = init[\"A\"]\n",
    "    rank = W.shape[1]\n",
    "    d = time_lags.shape[0]\n",
    "    mat_hat = np.zeros((W.shape[0], num_step, gibbs_iter))\n",
    "    for it in range(gibbs_iter):\n",
    "        W = sample_factor_w(mat, binary_mat, W, X, tau)\n",
    "        A, Sigma = sample_var_coefficient(X, time_lags)\n",
    "        X = sample_factor_x(sparse_mat, binary_mat, time_lags, W, X, tau, A, inv(Sigma))\n",
    "        X_new = X.copy()\n",
    "        for t in range(num_step):\n",
    "            var = X_new[X.shape[0] + t - 1 - time_lags, :].reshape([rank * d])\n",
    "            X_new = np.append(X_new, np.matmul(A.T, var).reshape([1, rank]), axis = 0)\n",
    "#         mat_hat[:, :, it] = np.random.normal(np.matmul(W, X_new[-1 - num_step : -1, :].T), 1 / tau) # dim1 * num_step\n",
    "        mat_hat[:, :, it] = np.matmul(W, X_new[-1 - num_step : -1, :].T) # dim1 * num_step\n",
    "    return mat_hat, W, X_new, tau, A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "               num_roll, start_time, num_step, burn_iter, gibbs_iter):\n",
    "    \n",
    "    W, X, tau, A = BTMF_burn(dense_mat[:, : start_time], sparse_mat[:, : start_time],\n",
    "                             init, time_lags, burn_iter)\n",
    "    result = np.zeros((W.shape[0], num_roll * num_step, gibbs_iter))\n",
    "    for t in range(num_roll):\n",
    "        mat = sparse_mat[:, : start_time + t * num_step]\n",
    "        print(mat.shape[1])\n",
    "        position = np.where(mat != 0)\n",
    "        binary_mat = mat.copy()\n",
    "        binary_mat[position] = 1\n",
    "        init = {\"W\": W, \"X\": X, \"tau\": tau, \"A\": A}\n",
    "        mat_hat, W, X, tau, A = BTMF_4cast(mat, binary_mat, \n",
    "                                           num_step, time_lags, init, gibbs_iter)\n",
    "        result[:, t * num_step : (t + 1) * num_step, :] = mat_hat\n",
    "        \n",
    "    mat_hat0 = np.mean(result, axis = 2)\n",
    "    small_dense_mat = dense_mat[:, start_time : dense_mat.shape[1]]\n",
    "    pos = np.where(small_dense_mat != 0)\n",
    "    final_mape = np.sum(np.abs(small_dense_mat[pos] - \n",
    "                               mat_hat0[pos]) / small_dense_mat[pos]) / small_dense_mat[pos].shape[0]\n",
    "    final_rmse = np.sqrt(np.sum((small_dense_mat[pos] - \n",
    "                                 mat_hat0[pos]) ** 2) / small_dense_mat[pos].shape[0])\n",
    "    print('Final MAPE: {:.6}'.format(final_mape))\n",
    "    print('Final RMSE: {:.6}'.format(final_rmse))\n",
    "    print()\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "\n",
    "tensor = scipy.io.loadmat('../datasets/Guangzhou-data-set/tensor.mat')\n",
    "tensor = tensor['tensor']\n",
    "random_matrix = scipy.io.loadmat('../datasets/Guangzhou-data-set/random_matrix.mat')\n",
    "random_matrix = random_matrix['random_matrix']\n",
    "random_tensor = scipy.io.loadmat('../datasets/Guangzhou-data-set/random_tensor.mat')\n",
    "random_tensor = random_tensor['random_tensor']\n",
    "\n",
    "dense_mat = tensor.reshape([tensor.shape[0], tensor.shape[1] * tensor.shape[2]])\n",
    "missing_rate = 0.4\n",
    "\n",
    "# =============================================================================\n",
    "### Random missing (RM) scenario\n",
    "### Set the RM scenario by:\n",
    "binary_mat = (np.round(random_tensor + 0.5 - missing_rate)\n",
    "              .reshape([random_tensor.shape[0], random_tensor.shape[1] * random_tensor.shape[2]]))\n",
    "# =============================================================================\n",
    "\n",
    "# binary_tensor = np.zeros(tensor.shape)\n",
    "# for i1 in range(tensor.shape[0]):\n",
    "#     for i2 in range(tensor.shape[1]):\n",
    "#         binary_tensor[i1, i2, :] = np.round(random_matrix[i1, i2] + 0.5 - missing_rate)\n",
    "# binary_mat = binary_tensor.reshape([binary_tensor.shape[0], binary_tensor.shape[1] * binary_tensor.shape[2]])\n",
    "\n",
    "sparse_mat = np.multiply(dense_mat, binary_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 5.94597\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 5.74879\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 5.70634\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 5.47132\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 4.99418\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 4.76256\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 4.68645\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 4.5744\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 4.55261\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 4.54463\n",
      "\n",
      "8064\n",
      "8070\n",
      "8076\n",
      "8082\n",
      "8088\n",
      "8094\n",
      "8100\n",
      "8106\n",
      "8112\n",
      "8118\n",
      "8124\n",
      "8130\n",
      "8136\n",
      "8142\n",
      "8148\n",
      "8154\n",
      "8160\n",
      "8166\n",
      "8172\n",
      "8178\n",
      "8184\n",
      "8190\n",
      "8196\n",
      "8202\n",
      "8208\n",
      "8214\n",
      "8220\n",
      "8226\n",
      "8232\n",
      "8238\n",
      "8244\n",
      "8250\n",
      "8256\n",
      "8262\n",
      "8268\n",
      "8274\n",
      "8280\n",
      "8286\n",
      "8292\n",
      "8298\n",
      "8304\n",
      "8310\n",
      "8316\n",
      "8322\n",
      "8328\n",
      "8334\n",
      "8340\n",
      "8346\n",
      "8352\n",
      "8358\n",
      "8364\n",
      "8370\n",
      "8376\n",
      "8382\n",
      "8388\n",
      "8394\n",
      "8400\n",
      "8406\n",
      "8412\n",
      "8418\n",
      "8424\n",
      "8430\n",
      "8436\n",
      "8442\n",
      "8448\n",
      "8454\n",
      "8460\n",
      "8466\n",
      "8472\n",
      "8478\n",
      "8484\n",
      "8490\n",
      "8496\n",
      "8502\n",
      "8508\n",
      "8514\n",
      "8520\n",
      "8526\n",
      "8532\n",
      "8538\n",
      "8544\n",
      "8550\n",
      "8556\n",
      "8562\n",
      "8568\n",
      "8574\n",
      "8580\n",
      "8586\n",
      "8592\n",
      "8598\n",
      "8604\n",
      "8610\n",
      "8616\n",
      "8622\n",
      "8628\n",
      "8634\n",
      "8640\n",
      "8646\n",
      "8652\n",
      "8658\n",
      "8664\n",
      "8670\n",
      "8676\n",
      "8682\n",
      "8688\n",
      "8694\n",
      "8700\n",
      "8706\n",
      "8712\n",
      "8718\n",
      "8724\n",
      "8730\n",
      "8736\n",
      "8742\n",
      "8748\n",
      "8754\n",
      "8760\n",
      "8766\n",
      "8772\n",
      "8778\n",
      "Final MAPE: 0.372138\n",
      "Final RMSE: 15.0209\n",
      "\n",
      "Running time: 762 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 144])\n",
    "num_step = 6\n",
    "num_roll = int(144 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 10\n",
    "gibbs_iter = 2\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 5.94449\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 5.75295\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 5.71641\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 5.53581\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 5.0634\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 4.88969\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 4.74457\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 4.68477\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 4.56635\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 4.54667\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: 4.53713\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: 4.50478\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: 4.44558\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: 4.41896\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: 4.40447\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: 4.39169\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: 4.3801\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: 4.36146\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: 4.34012\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: 4.323\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: 4.2991\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: 4.27874\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: 4.26798\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: 4.26194\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: 4.25591\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: 4.25072\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: 4.24422\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: 4.24307\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: 4.23493\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: 4.22458\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: 4.21628\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: 4.21207\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: 4.21048\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: 4.20769\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: 4.20458\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: 4.20501\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: 4.20187\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: 4.20378\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: 4.20147\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: 4.2014\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: 4.20172\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: 4.20174\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: 4.20179\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: 4.19926\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: 4.20019\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: 4.1975\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: 4.19601\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: 4.19907\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: 4.19479\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: 4.19641\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: 4.19439\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: 4.19538\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: 4.19394\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: 4.19151\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: 4.19388\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: 4.18899\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: 4.1936\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: 4.19189\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: 4.19198\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: 4.1927\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: 4.19205\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: 4.19358\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: 4.19379\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: 4.19318\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: 4.19543\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: 4.19417\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: 4.19487\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: 4.19499\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: 4.19354\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: 4.19311\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: 4.19313\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: 4.18999\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: 4.18869\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: 4.19073\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: 4.18876\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: 4.19048\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: 4.19235\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: 4.19325\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: 4.18861\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: 4.19046\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: 4.19224\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: 4.18991\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: 4.19028\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: 4.19048\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: 4.18996\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: 4.19008\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: 4.18816\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: 4.18801\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: 4.1857\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: 4.18845\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: 4.18824\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: 4.18866\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: 4.1874\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: 4.19071\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: 4.18984\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: 4.18867\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: 4.18954\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: 4.18876\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: 4.18756\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: 4.18824\n",
      "\n",
      "8064\n",
      "8070\n",
      "8076\n",
      "8082\n",
      "8088\n",
      "8094\n",
      "8100\n",
      "8106\n",
      "8112\n",
      "8118\n",
      "8124\n",
      "8130\n",
      "8136\n",
      "8142\n",
      "8148\n",
      "8154\n",
      "8160\n",
      "8166\n",
      "8172\n",
      "8178\n",
      "8184\n",
      "8190\n",
      "8196\n",
      "8202\n",
      "8208\n",
      "8214\n",
      "8220\n",
      "8226\n",
      "8232\n",
      "8238\n",
      "8244\n",
      "8250\n",
      "8256\n",
      "8262\n",
      "8268\n",
      "8274\n",
      "8280\n",
      "8286\n",
      "8292\n",
      "8298\n",
      "8304\n",
      "8310\n",
      "8316\n",
      "8322\n",
      "8328\n",
      "8334\n",
      "8340\n",
      "8346\n",
      "8352\n",
      "8358\n",
      "8364\n",
      "8370\n",
      "8376\n",
      "8382\n",
      "8388\n",
      "8394\n",
      "8400\n",
      "8406\n",
      "8412\n",
      "8418\n",
      "8424\n",
      "8430\n",
      "8436\n",
      "8442\n",
      "8448\n",
      "8454\n",
      "8460\n",
      "8466\n",
      "8472\n",
      "8478\n",
      "8484\n",
      "8490\n",
      "8496\n",
      "8502\n",
      "8508\n",
      "8514\n",
      "8520\n",
      "8526\n",
      "8532\n",
      "8538\n",
      "8544\n",
      "8550\n",
      "8556\n",
      "8562\n",
      "8568\n",
      "8574\n",
      "8580\n",
      "8586\n",
      "8592\n",
      "8598\n",
      "8604\n",
      "8610\n",
      "8616\n",
      "8622\n",
      "8628\n",
      "8634\n",
      "8640\n",
      "8646\n",
      "8652\n",
      "8658\n",
      "8664\n",
      "8670\n",
      "8676\n",
      "8682\n",
      "8688\n",
      "8694\n",
      "8700\n",
      "8706\n",
      "8712\n",
      "8718\n",
      "8724\n",
      "8730\n",
      "8736\n",
      "8742\n",
      "8748\n",
      "8754\n",
      "8760\n",
      "8766\n",
      "8772\n",
      "8778\n",
      "Final MAPE: 0.178763\n",
      "Final RMSE: 6.72478\n",
      "\n",
      "Running time: 6631 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 144])\n",
    "num_step = 6\n",
    "num_roll = int(144 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 100\n",
    "gibbs_iter = 20\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 5.93895\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 5.75626\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 5.70908\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 5.47771\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 5.05707\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 4.87126\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 4.72067\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 4.6074\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 4.55761\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 4.54906\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: 4.54095\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: 4.53278\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: 4.51274\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: 4.48254\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: 4.43496\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: 4.40604\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: 4.39511\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: 4.37981\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: 4.35406\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: 4.32049\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: 4.29999\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: 4.29119\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: 4.28679\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: 4.27596\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: 4.268\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: 4.25774\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: 4.25484\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: 4.24948\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: 4.24814\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: 4.24573\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: 4.24307\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: 4.23946\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: 4.23698\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: 4.22852\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: 4.22466\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: 4.22338\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: 4.21678\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: 4.21427\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: 4.20808\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: 4.20989\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: 4.20762\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: 4.20557\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: 4.20634\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: 4.20334\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: 4.20354\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: 4.19892\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: 4.20183\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: 4.19973\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: 4.19988\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: 4.19659\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: 4.19682\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: 4.19734\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: 4.19564\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: 4.19198\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: 4.19448\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: 4.19818\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: 4.19714\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: 4.19567\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: 4.19736\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: 4.19704\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: 4.19558\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: 4.19394\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: 4.19251\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: 4.19598\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: 4.19175\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: 4.19533\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: 4.1947\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: 4.19227\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: 4.1952\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: 4.19366\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: 4.19342\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: 4.19299\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: 4.19461\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: 4.19233\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: 4.19217\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: 4.19459\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: 4.19308\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: 4.19372\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: 4.1936\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: 4.19267\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: 4.19254\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: 4.1938\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: 4.19193\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: 4.19022\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: 4.19177\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: 4.19154\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: 4.19062\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: 4.19284\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: 4.18914\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: 4.18927\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: 4.19005\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: 4.18961\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: 4.18975\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: 4.19173\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: 4.19157\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: 4.18828\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: 4.18815\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: 4.18974\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: 4.18887\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: 4.18804\n",
      "\n",
      "Iteration: 101\n",
      "RMSE: 4.18748\n",
      "\n",
      "Iteration: 102\n",
      "RMSE: 4.18849\n",
      "\n",
      "Iteration: 103\n",
      "RMSE: 4.188\n",
      "\n",
      "Iteration: 104\n",
      "RMSE: 4.19015\n",
      "\n",
      "Iteration: 105\n",
      "RMSE: 4.18699\n",
      "\n",
      "Iteration: 106\n",
      "RMSE: 4.18692\n",
      "\n",
      "Iteration: 107\n",
      "RMSE: 4.1884\n",
      "\n",
      "Iteration: 108\n",
      "RMSE: 4.18753\n",
      "\n",
      "Iteration: 109\n",
      "RMSE: 4.18557\n",
      "\n",
      "Iteration: 110\n",
      "RMSE: 4.18822\n",
      "\n",
      "Iteration: 111\n",
      "RMSE: 4.189\n",
      "\n",
      "Iteration: 112\n",
      "RMSE: 4.1869\n",
      "\n",
      "Iteration: 113\n",
      "RMSE: 4.18694\n",
      "\n",
      "Iteration: 114\n",
      "RMSE: 4.18876\n",
      "\n",
      "Iteration: 115\n",
      "RMSE: 4.1872\n",
      "\n",
      "Iteration: 116\n",
      "RMSE: 4.18639\n",
      "\n",
      "Iteration: 117\n",
      "RMSE: 4.18803\n",
      "\n",
      "Iteration: 118\n",
      "RMSE: 4.18574\n",
      "\n",
      "Iteration: 119\n",
      "RMSE: 4.18825\n",
      "\n",
      "Iteration: 120\n",
      "RMSE: 4.18677\n",
      "\n",
      "Iteration: 121\n",
      "RMSE: 4.18598\n",
      "\n",
      "Iteration: 122\n",
      "RMSE: 4.18498\n",
      "\n",
      "Iteration: 123\n",
      "RMSE: 4.18506\n",
      "\n",
      "Iteration: 124\n",
      "RMSE: 4.18846\n",
      "\n",
      "Iteration: 125\n",
      "RMSE: 4.18845\n",
      "\n",
      "Iteration: 126\n",
      "RMSE: 4.18425\n",
      "\n",
      "Iteration: 127\n",
      "RMSE: 4.18349\n",
      "\n",
      "Iteration: 128\n",
      "RMSE: 4.18544\n",
      "\n",
      "Iteration: 129\n",
      "RMSE: 4.18539\n",
      "\n",
      "Iteration: 130\n",
      "RMSE: 4.18532\n",
      "\n",
      "Iteration: 131\n",
      "RMSE: 4.18514\n",
      "\n",
      "Iteration: 132\n",
      "RMSE: 4.18433\n",
      "\n",
      "Iteration: 133\n",
      "RMSE: 4.18594\n",
      "\n",
      "Iteration: 134\n",
      "RMSE: 4.18414\n",
      "\n",
      "Iteration: 135\n",
      "RMSE: 4.18297\n",
      "\n",
      "Iteration: 136\n",
      "RMSE: 4.18576\n",
      "\n",
      "Iteration: 137\n",
      "RMSE: 4.18116\n",
      "\n",
      "Iteration: 138\n",
      "RMSE: 4.1837\n",
      "\n",
      "Iteration: 139\n",
      "RMSE: 4.18314\n",
      "\n",
      "Iteration: 140\n",
      "RMSE: 4.18137\n",
      "\n",
      "Iteration: 141\n",
      "RMSE: 4.18295\n",
      "\n",
      "Iteration: 142\n",
      "RMSE: 4.18098\n",
      "\n",
      "Iteration: 143\n",
      "RMSE: 4.18215\n",
      "\n",
      "Iteration: 144\n",
      "RMSE: 4.18241\n",
      "\n",
      "Iteration: 145\n",
      "RMSE: 4.18162\n",
      "\n",
      "Iteration: 146\n",
      "RMSE: 4.18243\n",
      "\n",
      "Iteration: 147\n",
      "RMSE: 4.18267\n",
      "\n",
      "Iteration: 148\n",
      "RMSE: 4.18263\n",
      "\n",
      "Iteration: 149\n",
      "RMSE: 4.18137\n",
      "\n",
      "Iteration: 150\n",
      "RMSE: 4.18372\n",
      "\n",
      "Iteration: 151\n",
      "RMSE: 4.18208\n",
      "\n",
      "Iteration: 152\n",
      "RMSE: 4.17983\n",
      "\n",
      "Iteration: 153\n",
      "RMSE: 4.18229\n",
      "\n",
      "Iteration: 154\n",
      "RMSE: 4.18344\n",
      "\n",
      "Iteration: 155\n",
      "RMSE: 4.18001\n",
      "\n",
      "Iteration: 156\n",
      "RMSE: 4.17874\n",
      "\n",
      "Iteration: 157\n",
      "RMSE: 4.18139\n",
      "\n",
      "Iteration: 158\n",
      "RMSE: 4.18192\n",
      "\n",
      "Iteration: 159\n",
      "RMSE: 4.18291\n",
      "\n",
      "Iteration: 160\n",
      "RMSE: 4.18102\n",
      "\n",
      "Iteration: 161\n",
      "RMSE: 4.18168\n",
      "\n",
      "Iteration: 162\n",
      "RMSE: 4.18134\n",
      "\n",
      "Iteration: 163\n",
      "RMSE: 4.18262\n",
      "\n",
      "Iteration: 164\n",
      "RMSE: 4.18136\n",
      "\n",
      "Iteration: 165\n",
      "RMSE: 4.18115\n",
      "\n",
      "Iteration: 166\n",
      "RMSE: 4.18201\n",
      "\n",
      "Iteration: 167\n",
      "RMSE: 4.17968\n",
      "\n",
      "Iteration: 168\n",
      "RMSE: 4.18225\n",
      "\n",
      "Iteration: 169\n",
      "RMSE: 4.18097\n",
      "\n",
      "Iteration: 170\n",
      "RMSE: 4.1841\n",
      "\n",
      "Iteration: 171\n",
      "RMSE: 4.17984\n",
      "\n",
      "Iteration: 172\n",
      "RMSE: 4.1809\n",
      "\n",
      "Iteration: 173\n",
      "RMSE: 4.17986\n",
      "\n",
      "Iteration: 174\n",
      "RMSE: 4.17861\n",
      "\n",
      "Iteration: 175\n",
      "RMSE: 4.18045\n",
      "\n",
      "Iteration: 176\n",
      "RMSE: 4.17714\n",
      "\n",
      "Iteration: 177\n",
      "RMSE: 4.17921\n",
      "\n",
      "Iteration: 178\n",
      "RMSE: 4.18006\n",
      "\n",
      "Iteration: 179\n",
      "RMSE: 4.17881\n",
      "\n",
      "Iteration: 180\n",
      "RMSE: 4.17908\n",
      "\n",
      "Iteration: 181\n",
      "RMSE: 4.18011\n",
      "\n",
      "Iteration: 182\n",
      "RMSE: 4.18031\n",
      "\n",
      "Iteration: 183\n",
      "RMSE: 4.17814\n",
      "\n",
      "Iteration: 184\n",
      "RMSE: 4.17795\n",
      "\n",
      "Iteration: 185\n",
      "RMSE: 4.18009\n",
      "\n",
      "Iteration: 186\n",
      "RMSE: 4.18009\n",
      "\n",
      "Iteration: 187\n",
      "RMSE: 4.17787\n",
      "\n",
      "Iteration: 188\n",
      "RMSE: 4.17836\n",
      "\n",
      "Iteration: 189\n",
      "RMSE: 4.1789\n",
      "\n",
      "Iteration: 190\n",
      "RMSE: 4.17868\n",
      "\n",
      "Iteration: 191\n",
      "RMSE: 4.17927\n",
      "\n",
      "Iteration: 192\n",
      "RMSE: 4.17811\n",
      "\n",
      "Iteration: 193\n",
      "RMSE: 4.17838\n",
      "\n",
      "Iteration: 194\n",
      "RMSE: 4.17664\n",
      "\n",
      "Iteration: 195\n",
      "RMSE: 4.17891\n",
      "\n",
      "Iteration: 196\n",
      "RMSE: 4.17975\n",
      "\n",
      "Iteration: 197\n",
      "RMSE: 4.18044\n",
      "\n",
      "Iteration: 198\n",
      "RMSE: 4.18138\n",
      "\n",
      "Iteration: 199\n",
      "RMSE: 4.17869\n",
      "\n",
      "Iteration: 200\n",
      "RMSE: 4.17578\n",
      "\n",
      "Iteration: 201\n",
      "RMSE: 4.17624\n",
      "\n",
      "Iteration: 202\n",
      "RMSE: 4.17747\n",
      "\n",
      "Iteration: 203\n",
      "RMSE: 4.17532\n",
      "\n",
      "Iteration: 204\n",
      "RMSE: 4.17876\n",
      "\n",
      "Iteration: 205\n",
      "RMSE: 4.17715\n",
      "\n",
      "Iteration: 206\n",
      "RMSE: 4.17796\n",
      "\n",
      "Iteration: 207\n",
      "RMSE: 4.17551\n",
      "\n",
      "Iteration: 208\n",
      "RMSE: 4.17704\n",
      "\n",
      "Iteration: 209\n",
      "RMSE: 4.17478\n",
      "\n",
      "Iteration: 210\n",
      "RMSE: 4.17757\n",
      "\n",
      "Iteration: 211\n",
      "RMSE: 4.17695\n",
      "\n",
      "Iteration: 212\n",
      "RMSE: 4.17369\n",
      "\n",
      "Iteration: 213\n",
      "RMSE: 4.17359\n",
      "\n",
      "Iteration: 214\n",
      "RMSE: 4.17426\n",
      "\n",
      "Iteration: 215\n",
      "RMSE: 4.17247\n",
      "\n",
      "Iteration: 216\n",
      "RMSE: 4.17126\n",
      "\n",
      "Iteration: 217\n",
      "RMSE: 4.177\n",
      "\n",
      "Iteration: 218\n",
      "RMSE: 4.17701\n",
      "\n",
      "Iteration: 219\n",
      "RMSE: 4.17552\n",
      "\n",
      "Iteration: 220\n",
      "RMSE: 4.17676\n",
      "\n",
      "Iteration: 221\n",
      "RMSE: 4.17863\n",
      "\n",
      "Iteration: 222\n",
      "RMSE: 4.17941\n",
      "\n",
      "Iteration: 223\n",
      "RMSE: 4.17908\n",
      "\n",
      "Iteration: 224\n",
      "RMSE: 4.17827\n",
      "\n",
      "Iteration: 225\n",
      "RMSE: 4.17631\n",
      "\n",
      "Iteration: 226\n",
      "RMSE: 4.17672\n",
      "\n",
      "Iteration: 227\n",
      "RMSE: 4.1752\n",
      "\n",
      "Iteration: 228\n",
      "RMSE: 4.17723\n",
      "\n",
      "Iteration: 229\n",
      "RMSE: 4.17695\n",
      "\n",
      "Iteration: 230\n",
      "RMSE: 4.17613\n",
      "\n",
      "Iteration: 231\n",
      "RMSE: 4.17632\n",
      "\n",
      "Iteration: 232\n",
      "RMSE: 4.17808\n",
      "\n",
      "Iteration: 233\n",
      "RMSE: 4.17542\n",
      "\n",
      "Iteration: 234\n",
      "RMSE: 4.17551\n",
      "\n",
      "Iteration: 235\n",
      "RMSE: 4.17575\n",
      "\n",
      "Iteration: 236\n",
      "RMSE: 4.17817\n",
      "\n",
      "Iteration: 237\n",
      "RMSE: 4.17549\n",
      "\n",
      "Iteration: 238\n",
      "RMSE: 4.17589\n",
      "\n",
      "Iteration: 239\n",
      "RMSE: 4.1765\n",
      "\n",
      "Iteration: 240\n",
      "RMSE: 4.17623\n",
      "\n",
      "Iteration: 241\n",
      "RMSE: 4.17397\n",
      "\n",
      "Iteration: 242\n",
      "RMSE: 4.17509\n",
      "\n",
      "Iteration: 243\n",
      "RMSE: 4.17429\n",
      "\n",
      "Iteration: 244\n",
      "RMSE: 4.17529\n",
      "\n",
      "Iteration: 245\n",
      "RMSE: 4.17607\n",
      "\n",
      "Iteration: 246\n",
      "RMSE: 4.17392\n",
      "\n",
      "Iteration: 247\n",
      "RMSE: 4.17289\n",
      "\n",
      "Iteration: 248\n",
      "RMSE: 4.17157\n",
      "\n",
      "Iteration: 249\n",
      "RMSE: 4.17634\n",
      "\n",
      "Iteration: 250\n",
      "RMSE: 4.17411\n",
      "\n",
      "Iteration: 251\n",
      "RMSE: 4.17242\n",
      "\n",
      "Iteration: 252\n",
      "RMSE: 4.17225\n",
      "\n",
      "Iteration: 253\n",
      "RMSE: 4.17385\n",
      "\n",
      "Iteration: 254\n",
      "RMSE: 4.17513\n",
      "\n",
      "Iteration: 255\n",
      "RMSE: 4.17334\n",
      "\n",
      "Iteration: 256\n",
      "RMSE: 4.17315\n",
      "\n",
      "Iteration: 257\n",
      "RMSE: 4.17348\n",
      "\n",
      "Iteration: 258\n",
      "RMSE: 4.17558\n",
      "\n",
      "Iteration: 259\n",
      "RMSE: 4.17489\n",
      "\n",
      "Iteration: 260\n",
      "RMSE: 4.17453\n",
      "\n",
      "Iteration: 261\n",
      "RMSE: 4.17606\n",
      "\n",
      "Iteration: 262\n",
      "RMSE: 4.17288\n",
      "\n",
      "Iteration: 263\n",
      "RMSE: 4.17344\n",
      "\n",
      "Iteration: 264\n",
      "RMSE: 4.17338\n",
      "\n",
      "Iteration: 265\n",
      "RMSE: 4.17289\n",
      "\n",
      "Iteration: 266\n",
      "RMSE: 4.17387\n",
      "\n",
      "Iteration: 267\n",
      "RMSE: 4.17399\n",
      "\n",
      "Iteration: 268\n",
      "RMSE: 4.17473\n",
      "\n",
      "Iteration: 269\n",
      "RMSE: 4.17627\n",
      "\n",
      "Iteration: 270\n",
      "RMSE: 4.1739\n",
      "\n",
      "Iteration: 271\n",
      "RMSE: 4.17374\n",
      "\n",
      "Iteration: 272\n",
      "RMSE: 4.17678\n",
      "\n",
      "Iteration: 273\n",
      "RMSE: 4.17561\n",
      "\n",
      "Iteration: 274\n",
      "RMSE: 4.17334\n",
      "\n",
      "Iteration: 275\n",
      "RMSE: 4.17215\n",
      "\n",
      "Iteration: 276\n",
      "RMSE: 4.1725\n",
      "\n",
      "Iteration: 277\n",
      "RMSE: 4.17401\n",
      "\n",
      "Iteration: 278\n",
      "RMSE: 4.17075\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 279\n",
      "RMSE: 4.17269\n",
      "\n",
      "Iteration: 280\n",
      "RMSE: 4.17289\n",
      "\n",
      "Iteration: 281\n",
      "RMSE: 4.17093\n",
      "\n",
      "Iteration: 282\n",
      "RMSE: 4.16826\n",
      "\n",
      "Iteration: 283\n",
      "RMSE: 4.17359\n",
      "\n",
      "Iteration: 284\n",
      "RMSE: 4.17055\n",
      "\n",
      "Iteration: 285\n",
      "RMSE: 4.17155\n",
      "\n",
      "Iteration: 286\n",
      "RMSE: 4.17145\n",
      "\n",
      "Iteration: 287\n",
      "RMSE: 4.16986\n",
      "\n",
      "Iteration: 288\n",
      "RMSE: 4.16994\n",
      "\n",
      "Iteration: 289\n",
      "RMSE: 4.17305\n",
      "\n",
      "Iteration: 290\n",
      "RMSE: 4.1739\n",
      "\n",
      "Iteration: 291\n",
      "RMSE: 4.17216\n",
      "\n",
      "Iteration: 292\n",
      "RMSE: 4.1747\n",
      "\n",
      "Iteration: 293\n",
      "RMSE: 4.17331\n",
      "\n",
      "Iteration: 294\n",
      "RMSE: 4.17382\n",
      "\n",
      "Iteration: 295\n",
      "RMSE: 4.17009\n",
      "\n",
      "Iteration: 296\n",
      "RMSE: 4.172\n",
      "\n",
      "Iteration: 297\n",
      "RMSE: 4.174\n",
      "\n",
      "Iteration: 298\n",
      "RMSE: 4.17279\n",
      "\n",
      "Iteration: 299\n",
      "RMSE: 4.17181\n",
      "\n",
      "Iteration: 300\n",
      "RMSE: 4.17332\n",
      "\n",
      "Iteration: 301\n",
      "RMSE: 4.17236\n",
      "\n",
      "Iteration: 302\n",
      "RMSE: 4.17359\n",
      "\n",
      "Iteration: 303\n",
      "RMSE: 4.17273\n",
      "\n",
      "Iteration: 304\n",
      "RMSE: 4.17165\n",
      "\n",
      "Iteration: 305\n",
      "RMSE: 4.17166\n",
      "\n",
      "Iteration: 306\n",
      "RMSE: 4.17236\n",
      "\n",
      "Iteration: 307\n",
      "RMSE: 4.17234\n",
      "\n",
      "Iteration: 308\n",
      "RMSE: 4.17236\n",
      "\n",
      "Iteration: 309\n",
      "RMSE: 4.17428\n",
      "\n",
      "Iteration: 310\n",
      "RMSE: 4.17245\n",
      "\n",
      "Iteration: 311\n",
      "RMSE: 4.17205\n",
      "\n",
      "Iteration: 312\n",
      "RMSE: 4.171\n",
      "\n",
      "Iteration: 313\n",
      "RMSE: 4.17249\n",
      "\n",
      "Iteration: 314\n",
      "RMSE: 4.17232\n",
      "\n",
      "Iteration: 315\n",
      "RMSE: 4.17093\n",
      "\n",
      "Iteration: 316\n",
      "RMSE: 4.17175\n",
      "\n",
      "Iteration: 317\n",
      "RMSE: 4.16898\n",
      "\n",
      "Iteration: 318\n",
      "RMSE: 4.17128\n",
      "\n",
      "Iteration: 319\n",
      "RMSE: 4.17105\n",
      "\n",
      "Iteration: 320\n",
      "RMSE: 4.17003\n",
      "\n",
      "Iteration: 321\n",
      "RMSE: 4.16914\n",
      "\n",
      "Iteration: 322\n",
      "RMSE: 4.17083\n",
      "\n",
      "Iteration: 323\n",
      "RMSE: 4.16978\n",
      "\n",
      "Iteration: 324\n",
      "RMSE: 4.17017\n",
      "\n",
      "Iteration: 325\n",
      "RMSE: 4.17097\n",
      "\n",
      "Iteration: 326\n",
      "RMSE: 4.16986\n",
      "\n",
      "Iteration: 327\n",
      "RMSE: 4.1682\n",
      "\n",
      "Iteration: 328\n",
      "RMSE: 4.16749\n",
      "\n",
      "Iteration: 329\n",
      "RMSE: 4.16929\n",
      "\n",
      "Iteration: 330\n",
      "RMSE: 4.16873\n",
      "\n",
      "Iteration: 331\n",
      "RMSE: 4.17118\n",
      "\n",
      "Iteration: 332\n",
      "RMSE: 4.17154\n",
      "\n",
      "Iteration: 333\n",
      "RMSE: 4.17001\n",
      "\n",
      "Iteration: 334\n",
      "RMSE: 4.1708\n",
      "\n",
      "Iteration: 335\n",
      "RMSE: 4.17264\n",
      "\n",
      "Iteration: 336\n",
      "RMSE: 4.17023\n",
      "\n",
      "Iteration: 337\n",
      "RMSE: 4.16931\n",
      "\n",
      "Iteration: 338\n",
      "RMSE: 4.16813\n",
      "\n",
      "Iteration: 339\n",
      "RMSE: 4.16789\n",
      "\n",
      "Iteration: 340\n",
      "RMSE: 4.16668\n",
      "\n",
      "Iteration: 341\n",
      "RMSE: 4.17025\n",
      "\n",
      "Iteration: 342\n",
      "RMSE: 4.16777\n",
      "\n",
      "Iteration: 343\n",
      "RMSE: 4.1675\n",
      "\n",
      "Iteration: 344\n",
      "RMSE: 4.1687\n",
      "\n",
      "Iteration: 345\n",
      "RMSE: 4.16835\n",
      "\n",
      "Iteration: 346\n",
      "RMSE: 4.16751\n",
      "\n",
      "Iteration: 347\n",
      "RMSE: 4.16978\n",
      "\n",
      "Iteration: 348\n",
      "RMSE: 4.16877\n",
      "\n",
      "Iteration: 349\n",
      "RMSE: 4.1689\n",
      "\n",
      "Iteration: 350\n",
      "RMSE: 4.16963\n",
      "\n",
      "Iteration: 351\n",
      "RMSE: 4.16777\n",
      "\n",
      "Iteration: 352\n",
      "RMSE: 4.16809\n",
      "\n",
      "Iteration: 353\n",
      "RMSE: 4.16797\n",
      "\n",
      "Iteration: 354\n",
      "RMSE: 4.16736\n",
      "\n",
      "Iteration: 355\n",
      "RMSE: 4.1671\n",
      "\n",
      "Iteration: 356\n",
      "RMSE: 4.16618\n",
      "\n",
      "Iteration: 357\n",
      "RMSE: 4.1656\n",
      "\n",
      "Iteration: 358\n",
      "RMSE: 4.1659\n",
      "\n",
      "Iteration: 359\n",
      "RMSE: 4.16696\n",
      "\n",
      "Iteration: 360\n",
      "RMSE: 4.16637\n",
      "\n",
      "Iteration: 361\n",
      "RMSE: 4.16601\n",
      "\n",
      "Iteration: 362\n",
      "RMSE: 4.16693\n",
      "\n",
      "Iteration: 363\n",
      "RMSE: 4.16618\n",
      "\n",
      "Iteration: 364\n",
      "RMSE: 4.16718\n",
      "\n",
      "Iteration: 365\n",
      "RMSE: 4.16688\n",
      "\n",
      "Iteration: 366\n",
      "RMSE: 4.16519\n",
      "\n",
      "Iteration: 367\n",
      "RMSE: 4.16792\n",
      "\n",
      "Iteration: 368\n",
      "RMSE: 4.16583\n",
      "\n",
      "Iteration: 369\n",
      "RMSE: 4.16547\n",
      "\n",
      "Iteration: 370\n",
      "RMSE: 4.16399\n",
      "\n",
      "Iteration: 371\n",
      "RMSE: 4.16468\n",
      "\n",
      "Iteration: 372\n",
      "RMSE: 4.16694\n",
      "\n",
      "Iteration: 373\n",
      "RMSE: 4.16725\n",
      "\n",
      "Iteration: 374\n",
      "RMSE: 4.16577\n",
      "\n",
      "Iteration: 375\n",
      "RMSE: 4.16579\n",
      "\n",
      "Iteration: 376\n",
      "RMSE: 4.16584\n",
      "\n",
      "Iteration: 377\n",
      "RMSE: 4.16751\n",
      "\n",
      "Iteration: 378\n",
      "RMSE: 4.16708\n",
      "\n",
      "Iteration: 379\n",
      "RMSE: 4.16637\n",
      "\n",
      "Iteration: 380\n",
      "RMSE: 4.1665\n",
      "\n",
      "Iteration: 381\n",
      "RMSE: 4.16789\n",
      "\n",
      "Iteration: 382\n",
      "RMSE: 4.16743\n",
      "\n",
      "Iteration: 383\n",
      "RMSE: 4.16706\n",
      "\n",
      "Iteration: 384\n",
      "RMSE: 4.16624\n",
      "\n",
      "Iteration: 385\n",
      "RMSE: 4.16684\n",
      "\n",
      "Iteration: 386\n",
      "RMSE: 4.16697\n",
      "\n",
      "Iteration: 387\n",
      "RMSE: 4.16894\n",
      "\n",
      "Iteration: 388\n",
      "RMSE: 4.16874\n",
      "\n",
      "Iteration: 389\n",
      "RMSE: 4.16899\n",
      "\n",
      "Iteration: 390\n",
      "RMSE: 4.16905\n",
      "\n",
      "Iteration: 391\n",
      "RMSE: 4.16961\n",
      "\n",
      "Iteration: 392\n",
      "RMSE: 4.16781\n",
      "\n",
      "Iteration: 393\n",
      "RMSE: 4.16878\n",
      "\n",
      "Iteration: 394\n",
      "RMSE: 4.16832\n",
      "\n",
      "Iteration: 395\n",
      "RMSE: 4.16762\n",
      "\n",
      "Iteration: 396\n",
      "RMSE: 4.16623\n",
      "\n",
      "Iteration: 397\n",
      "RMSE: 4.16665\n",
      "\n",
      "Iteration: 398\n",
      "RMSE: 4.16558\n",
      "\n",
      "Iteration: 399\n",
      "RMSE: 4.16722\n",
      "\n",
      "Iteration: 400\n",
      "RMSE: 4.16444\n",
      "\n",
      "Iteration: 401\n",
      "RMSE: 4.16517\n",
      "\n",
      "Iteration: 402\n",
      "RMSE: 4.16674\n",
      "\n",
      "Iteration: 403\n",
      "RMSE: 4.16591\n",
      "\n",
      "Iteration: 404\n",
      "RMSE: 4.16632\n",
      "\n",
      "Iteration: 405\n",
      "RMSE: 4.16617\n",
      "\n",
      "Iteration: 406\n",
      "RMSE: 4.16708\n",
      "\n",
      "Iteration: 407\n",
      "RMSE: 4.16571\n",
      "\n",
      "Iteration: 408\n",
      "RMSE: 4.16768\n",
      "\n",
      "Iteration: 409\n",
      "RMSE: 4.16844\n",
      "\n",
      "Iteration: 410\n",
      "RMSE: 4.16772\n",
      "\n",
      "Iteration: 411\n",
      "RMSE: 4.16555\n",
      "\n",
      "Iteration: 412\n",
      "RMSE: 4.16743\n",
      "\n",
      "Iteration: 413\n",
      "RMSE: 4.16563\n",
      "\n",
      "Iteration: 414\n",
      "RMSE: 4.1675\n",
      "\n",
      "Iteration: 415\n",
      "RMSE: 4.16743\n",
      "\n",
      "Iteration: 416\n",
      "RMSE: 4.16605\n",
      "\n",
      "Iteration: 417\n",
      "RMSE: 4.16326\n",
      "\n",
      "Iteration: 418\n",
      "RMSE: 4.16383\n",
      "\n",
      "Iteration: 419\n",
      "RMSE: 4.16552\n",
      "\n",
      "Iteration: 420\n",
      "RMSE: 4.16279\n",
      "\n",
      "Iteration: 421\n",
      "RMSE: 4.16415\n",
      "\n",
      "Iteration: 422\n",
      "RMSE: 4.16367\n",
      "\n",
      "Iteration: 423\n",
      "RMSE: 4.16418\n",
      "\n",
      "Iteration: 424\n",
      "RMSE: 4.16417\n",
      "\n",
      "Iteration: 425\n",
      "RMSE: 4.16372\n",
      "\n",
      "Iteration: 426\n",
      "RMSE: 4.16442\n",
      "\n",
      "Iteration: 427\n",
      "RMSE: 4.16545\n",
      "\n",
      "Iteration: 428\n",
      "RMSE: 4.16462\n",
      "\n",
      "Iteration: 429\n",
      "RMSE: 4.16555\n",
      "\n",
      "Iteration: 430\n",
      "RMSE: 4.16425\n",
      "\n",
      "Iteration: 431\n",
      "RMSE: 4.16431\n",
      "\n",
      "Iteration: 432\n",
      "RMSE: 4.16681\n",
      "\n",
      "Iteration: 433\n",
      "RMSE: 4.16657\n",
      "\n",
      "Iteration: 434\n",
      "RMSE: 4.16499\n",
      "\n",
      "Iteration: 435\n",
      "RMSE: 4.16477\n",
      "\n",
      "Iteration: 436\n",
      "RMSE: 4.16458\n",
      "\n",
      "Iteration: 437\n",
      "RMSE: 4.16168\n",
      "\n",
      "Iteration: 438\n",
      "RMSE: 4.16246\n",
      "\n",
      "Iteration: 439\n",
      "RMSE: 4.16225\n",
      "\n",
      "Iteration: 440\n",
      "RMSE: 4.16225\n",
      "\n",
      "Iteration: 441\n",
      "RMSE: 4.16407\n",
      "\n",
      "Iteration: 442\n",
      "RMSE: 4.16112\n",
      "\n",
      "Iteration: 443\n",
      "RMSE: 4.16249\n",
      "\n",
      "Iteration: 444\n",
      "RMSE: 4.16291\n",
      "\n",
      "Iteration: 445\n",
      "RMSE: 4.16253\n",
      "\n",
      "Iteration: 446\n",
      "RMSE: 4.16451\n",
      "\n",
      "Iteration: 447\n",
      "RMSE: 4.16368\n",
      "\n",
      "Iteration: 448\n",
      "RMSE: 4.16489\n",
      "\n",
      "Iteration: 449\n",
      "RMSE: 4.16381\n",
      "\n",
      "Iteration: 450\n",
      "RMSE: 4.16302\n",
      "\n",
      "Iteration: 451\n",
      "RMSE: 4.163\n",
      "\n",
      "Iteration: 452\n",
      "RMSE: 4.16421\n",
      "\n",
      "Iteration: 453\n",
      "RMSE: 4.16465\n",
      "\n",
      "Iteration: 454\n",
      "RMSE: 4.1636\n",
      "\n",
      "Iteration: 455\n",
      "RMSE: 4.1642\n",
      "\n",
      "Iteration: 456\n",
      "RMSE: 4.16564\n",
      "\n",
      "Iteration: 457\n",
      "RMSE: 4.16436\n",
      "\n",
      "Iteration: 458\n",
      "RMSE: 4.16503\n",
      "\n",
      "Iteration: 459\n",
      "RMSE: 4.16319\n",
      "\n",
      "Iteration: 460\n",
      "RMSE: 4.16312\n",
      "\n",
      "Iteration: 461\n",
      "RMSE: 4.16486\n",
      "\n",
      "Iteration: 462\n",
      "RMSE: 4.16428\n",
      "\n",
      "Iteration: 463\n",
      "RMSE: 4.16379\n",
      "\n",
      "Iteration: 464\n",
      "RMSE: 4.16337\n",
      "\n",
      "Iteration: 465\n",
      "RMSE: 4.16406\n",
      "\n",
      "Iteration: 466\n",
      "RMSE: 4.16658\n",
      "\n",
      "Iteration: 467\n",
      "RMSE: 4.16517\n",
      "\n",
      "Iteration: 468\n",
      "RMSE: 4.16659\n",
      "\n",
      "Iteration: 469\n",
      "RMSE: 4.16484\n",
      "\n",
      "Iteration: 470\n",
      "RMSE: 4.16298\n",
      "\n",
      "Iteration: 471\n",
      "RMSE: 4.1631\n",
      "\n",
      "Iteration: 472\n",
      "RMSE: 4.1661\n",
      "\n",
      "Iteration: 473\n",
      "RMSE: 4.16564\n",
      "\n",
      "Iteration: 474\n",
      "RMSE: 4.16446\n",
      "\n",
      "Iteration: 475\n",
      "RMSE: 4.16275\n",
      "\n",
      "Iteration: 476\n",
      "RMSE: 4.16292\n",
      "\n",
      "Iteration: 477\n",
      "RMSE: 4.16035\n",
      "\n",
      "Iteration: 478\n",
      "RMSE: 4.16126\n",
      "\n",
      "Iteration: 479\n",
      "RMSE: 4.16133\n",
      "\n",
      "Iteration: 480\n",
      "RMSE: 4.16026\n",
      "\n",
      "Iteration: 481\n",
      "RMSE: 4.16129\n",
      "\n",
      "Iteration: 482\n",
      "RMSE: 4.16133\n",
      "\n",
      "Iteration: 483\n",
      "RMSE: 4.16274\n",
      "\n",
      "Iteration: 484\n",
      "RMSE: 4.16192\n",
      "\n",
      "Iteration: 485\n",
      "RMSE: 4.16262\n",
      "\n",
      "Iteration: 486\n",
      "RMSE: 4.16308\n",
      "\n",
      "Iteration: 487\n",
      "RMSE: 4.16263\n",
      "\n",
      "Iteration: 488\n",
      "RMSE: 4.16222\n",
      "\n",
      "Iteration: 489\n",
      "RMSE: 4.16207\n",
      "\n",
      "Iteration: 490\n",
      "RMSE: 4.16218\n",
      "\n",
      "Iteration: 491\n",
      "RMSE: 4.16179\n",
      "\n",
      "Iteration: 492\n",
      "RMSE: 4.1642\n",
      "\n",
      "Iteration: 493\n",
      "RMSE: 4.16363\n",
      "\n",
      "Iteration: 494\n",
      "RMSE: 4.16102\n",
      "\n",
      "Iteration: 495\n",
      "RMSE: 4.16284\n",
      "\n",
      "Iteration: 496\n",
      "RMSE: 4.16171\n",
      "\n",
      "Iteration: 497\n",
      "RMSE: 4.1652\n",
      "\n",
      "Iteration: 498\n",
      "RMSE: 4.16433\n",
      "\n",
      "Iteration: 499\n",
      "RMSE: 4.16273\n",
      "\n",
      "Iteration: 500\n",
      "RMSE: 4.16107\n",
      "\n",
      "Iteration: 501\n",
      "RMSE: 4.16232\n",
      "\n",
      "Iteration: 502\n",
      "RMSE: 4.1618\n",
      "\n",
      "Iteration: 503\n",
      "RMSE: 4.16223\n",
      "\n",
      "Iteration: 504\n",
      "RMSE: 4.16168\n",
      "\n",
      "Iteration: 505\n",
      "RMSE: 4.16284\n",
      "\n",
      "Iteration: 506\n",
      "RMSE: 4.16378\n",
      "\n",
      "Iteration: 507\n",
      "RMSE: 4.16212\n",
      "\n",
      "Iteration: 508\n",
      "RMSE: 4.16422\n",
      "\n",
      "Iteration: 509\n",
      "RMSE: 4.16234\n",
      "\n",
      "Iteration: 510\n",
      "RMSE: 4.16324\n",
      "\n",
      "Iteration: 511\n",
      "RMSE: 4.16225\n",
      "\n",
      "Iteration: 512\n",
      "RMSE: 4.16082\n",
      "\n",
      "Iteration: 513\n",
      "RMSE: 4.163\n",
      "\n",
      "Iteration: 514\n",
      "RMSE: 4.16321\n",
      "\n",
      "Iteration: 515\n",
      "RMSE: 4.16434\n",
      "\n",
      "Iteration: 516\n",
      "RMSE: 4.16235\n",
      "\n",
      "Iteration: 517\n",
      "RMSE: 4.1636\n",
      "\n",
      "Iteration: 518\n",
      "RMSE: 4.16216\n",
      "\n",
      "Iteration: 519\n",
      "RMSE: 4.16235\n",
      "\n",
      "Iteration: 520\n",
      "RMSE: 4.16234\n",
      "\n",
      "Iteration: 521\n",
      "RMSE: 4.16288\n",
      "\n",
      "Iteration: 522\n",
      "RMSE: 4.16282\n",
      "\n",
      "Iteration: 523\n",
      "RMSE: 4.16184\n",
      "\n",
      "Iteration: 524\n",
      "RMSE: 4.16182\n",
      "\n",
      "Iteration: 525\n",
      "RMSE: 4.16098\n",
      "\n",
      "Iteration: 526\n",
      "RMSE: 4.16173\n",
      "\n",
      "Iteration: 527\n",
      "RMSE: 4.15926\n",
      "\n",
      "Iteration: 528\n",
      "RMSE: 4.16168\n",
      "\n",
      "Iteration: 529\n",
      "RMSE: 4.16106\n",
      "\n",
      "Iteration: 530\n",
      "RMSE: 4.15992\n",
      "\n",
      "Iteration: 531\n",
      "RMSE: 4.16317\n",
      "\n",
      "Iteration: 532\n",
      "RMSE: 4.16298\n",
      "\n",
      "Iteration: 533\n",
      "RMSE: 4.16369\n",
      "\n",
      "Iteration: 534\n",
      "RMSE: 4.16314\n",
      "\n",
      "Iteration: 535\n",
      "RMSE: 4.16304\n",
      "\n",
      "Iteration: 536\n",
      "RMSE: 4.16304\n",
      "\n",
      "Iteration: 537\n",
      "RMSE: 4.16133\n",
      "\n",
      "Iteration: 538\n",
      "RMSE: 4.16195\n",
      "\n",
      "Iteration: 539\n",
      "RMSE: 4.16294\n",
      "\n",
      "Iteration: 540\n",
      "RMSE: 4.16286\n",
      "\n",
      "Iteration: 541\n",
      "RMSE: 4.16243\n",
      "\n",
      "Iteration: 542\n",
      "RMSE: 4.16176\n",
      "\n",
      "Iteration: 543\n",
      "RMSE: 4.16272\n",
      "\n",
      "Iteration: 544\n",
      "RMSE: 4.15979\n",
      "\n",
      "Iteration: 545\n",
      "RMSE: 4.16191\n",
      "\n",
      "Iteration: 546\n",
      "RMSE: 4.16243\n",
      "\n",
      "Iteration: 547\n",
      "RMSE: 4.16039\n",
      "\n",
      "Iteration: 548\n",
      "RMSE: 4.15978\n",
      "\n",
      "Iteration: 549\n",
      "RMSE: 4.16092\n",
      "\n",
      "Iteration: 550\n",
      "RMSE: 4.15984\n",
      "\n",
      "Iteration: 551\n",
      "RMSE: 4.1623\n",
      "\n",
      "Iteration: 552\n",
      "RMSE: 4.16409\n",
      "\n",
      "Iteration: 553\n",
      "RMSE: 4.16033\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 554\n",
      "RMSE: 4.16119\n",
      "\n",
      "Iteration: 555\n",
      "RMSE: 4.15966\n",
      "\n",
      "Iteration: 556\n",
      "RMSE: 4.15945\n",
      "\n",
      "Iteration: 557\n",
      "RMSE: 4.16213\n",
      "\n",
      "Iteration: 558\n",
      "RMSE: 4.15928\n",
      "\n",
      "Iteration: 559\n",
      "RMSE: 4.16085\n",
      "\n",
      "Iteration: 560\n",
      "RMSE: 4.16203\n",
      "\n",
      "Iteration: 561\n",
      "RMSE: 4.16011\n",
      "\n",
      "Iteration: 562\n",
      "RMSE: 4.15991\n",
      "\n",
      "Iteration: 563\n",
      "RMSE: 4.15951\n",
      "\n",
      "Iteration: 564\n",
      "RMSE: 4.1596\n",
      "\n",
      "Iteration: 565\n",
      "RMSE: 4.16355\n",
      "\n",
      "Iteration: 566\n",
      "RMSE: 4.15974\n",
      "\n",
      "Iteration: 567\n",
      "RMSE: 4.15856\n",
      "\n",
      "Iteration: 568\n",
      "RMSE: 4.15861\n",
      "\n",
      "Iteration: 569\n",
      "RMSE: 4.15716\n",
      "\n",
      "Iteration: 570\n",
      "RMSE: 4.15849\n",
      "\n",
      "Iteration: 571\n",
      "RMSE: 4.16046\n",
      "\n",
      "Iteration: 572\n",
      "RMSE: 4.16011\n",
      "\n",
      "Iteration: 573\n",
      "RMSE: 4.15921\n",
      "\n",
      "Iteration: 574\n",
      "RMSE: 4.15938\n",
      "\n",
      "Iteration: 575\n",
      "RMSE: 4.16154\n",
      "\n",
      "Iteration: 576\n",
      "RMSE: 4.16154\n",
      "\n",
      "Iteration: 577\n",
      "RMSE: 4.15887\n",
      "\n",
      "Iteration: 578\n",
      "RMSE: 4.1588\n",
      "\n",
      "Iteration: 579\n",
      "RMSE: 4.15796\n",
      "\n",
      "Iteration: 580\n",
      "RMSE: 4.15974\n",
      "\n",
      "Iteration: 581\n",
      "RMSE: 4.15819\n",
      "\n",
      "Iteration: 582\n",
      "RMSE: 4.15807\n",
      "\n",
      "Iteration: 583\n",
      "RMSE: 4.15667\n",
      "\n",
      "Iteration: 584\n",
      "RMSE: 4.15733\n",
      "\n",
      "Iteration: 585\n",
      "RMSE: 4.15993\n",
      "\n",
      "Iteration: 586\n",
      "RMSE: 4.16053\n",
      "\n",
      "Iteration: 587\n",
      "RMSE: 4.16118\n",
      "\n",
      "Iteration: 588\n",
      "RMSE: 4.16026\n",
      "\n",
      "Iteration: 589\n",
      "RMSE: 4.15987\n",
      "\n",
      "Iteration: 590\n",
      "RMSE: 4.15952\n",
      "\n",
      "Iteration: 591\n",
      "RMSE: 4.15682\n",
      "\n",
      "Iteration: 592\n",
      "RMSE: 4.15832\n",
      "\n",
      "Iteration: 593\n",
      "RMSE: 4.15833\n",
      "\n",
      "Iteration: 594\n",
      "RMSE: 4.1577\n",
      "\n",
      "Iteration: 595\n",
      "RMSE: 4.15775\n",
      "\n",
      "Iteration: 596\n",
      "RMSE: 4.15642\n",
      "\n",
      "Iteration: 597\n",
      "RMSE: 4.15571\n",
      "\n",
      "Iteration: 598\n",
      "RMSE: 4.1577\n",
      "\n",
      "Iteration: 599\n",
      "RMSE: 4.15653\n",
      "\n",
      "Iteration: 600\n",
      "RMSE: 4.15757\n",
      "\n",
      "Iteration: 601\n",
      "RMSE: 4.15906\n",
      "\n",
      "Iteration: 602\n",
      "RMSE: 4.16079\n",
      "\n",
      "Iteration: 603\n",
      "RMSE: 4.15945\n",
      "\n",
      "Iteration: 604\n",
      "RMSE: 4.15811\n",
      "\n",
      "Iteration: 605\n",
      "RMSE: 4.1588\n",
      "\n",
      "Iteration: 606\n",
      "RMSE: 4.15881\n",
      "\n",
      "Iteration: 607\n",
      "RMSE: 4.15717\n",
      "\n",
      "Iteration: 608\n",
      "RMSE: 4.15933\n",
      "\n",
      "Iteration: 609\n",
      "RMSE: 4.15987\n",
      "\n",
      "Iteration: 610\n",
      "RMSE: 4.15728\n",
      "\n",
      "Iteration: 611\n",
      "RMSE: 4.15994\n",
      "\n",
      "Iteration: 612\n",
      "RMSE: 4.15902\n",
      "\n",
      "Iteration: 613\n",
      "RMSE: 4.15852\n",
      "\n",
      "Iteration: 614\n",
      "RMSE: 4.15839\n",
      "\n",
      "Iteration: 615\n",
      "RMSE: 4.1578\n",
      "\n",
      "Iteration: 616\n",
      "RMSE: 4.15797\n",
      "\n",
      "Iteration: 617\n",
      "RMSE: 4.15774\n",
      "\n",
      "Iteration: 618\n",
      "RMSE: 4.15835\n",
      "\n",
      "Iteration: 619\n",
      "RMSE: 4.15824\n",
      "\n",
      "Iteration: 620\n",
      "RMSE: 4.15705\n",
      "\n",
      "Iteration: 621\n",
      "RMSE: 4.15726\n",
      "\n",
      "Iteration: 622\n",
      "RMSE: 4.15782\n",
      "\n",
      "Iteration: 623\n",
      "RMSE: 4.15857\n",
      "\n",
      "Iteration: 624\n",
      "RMSE: 4.15799\n",
      "\n",
      "Iteration: 625\n",
      "RMSE: 4.15884\n",
      "\n",
      "Iteration: 626\n",
      "RMSE: 4.16054\n",
      "\n",
      "Iteration: 627\n",
      "RMSE: 4.15902\n",
      "\n",
      "Iteration: 628\n",
      "RMSE: 4.15699\n",
      "\n",
      "Iteration: 629\n",
      "RMSE: 4.16109\n",
      "\n",
      "Iteration: 630\n",
      "RMSE: 4.15861\n",
      "\n",
      "Iteration: 631\n",
      "RMSE: 4.15917\n",
      "\n",
      "Iteration: 632\n",
      "RMSE: 4.15887\n",
      "\n",
      "Iteration: 633\n",
      "RMSE: 4.15647\n",
      "\n",
      "Iteration: 634\n",
      "RMSE: 4.15823\n",
      "\n",
      "Iteration: 635\n",
      "RMSE: 4.16028\n",
      "\n",
      "Iteration: 636\n",
      "RMSE: 4.1601\n",
      "\n",
      "Iteration: 637\n",
      "RMSE: 4.15742\n",
      "\n",
      "Iteration: 638\n",
      "RMSE: 4.15817\n",
      "\n",
      "Iteration: 639\n",
      "RMSE: 4.15769\n",
      "\n",
      "Iteration: 640\n",
      "RMSE: 4.15625\n",
      "\n",
      "Iteration: 641\n",
      "RMSE: 4.15763\n",
      "\n",
      "Iteration: 642\n",
      "RMSE: 4.15804\n",
      "\n",
      "Iteration: 643\n",
      "RMSE: 4.15785\n",
      "\n",
      "Iteration: 644\n",
      "RMSE: 4.15737\n",
      "\n",
      "Iteration: 645\n",
      "RMSE: 4.15898\n",
      "\n",
      "Iteration: 646\n",
      "RMSE: 4.15838\n",
      "\n",
      "Iteration: 647\n",
      "RMSE: 4.15853\n",
      "\n",
      "Iteration: 648\n",
      "RMSE: 4.15881\n",
      "\n",
      "Iteration: 649\n",
      "RMSE: 4.15838\n",
      "\n",
      "Iteration: 650\n",
      "RMSE: 4.16069\n",
      "\n",
      "Iteration: 651\n",
      "RMSE: 4.15955\n",
      "\n",
      "Iteration: 652\n",
      "RMSE: 4.15669\n",
      "\n",
      "Iteration: 653\n",
      "RMSE: 4.15708\n",
      "\n",
      "Iteration: 654\n",
      "RMSE: 4.15769\n",
      "\n",
      "Iteration: 655\n",
      "RMSE: 4.15694\n",
      "\n",
      "Iteration: 656\n",
      "RMSE: 4.157\n",
      "\n",
      "Iteration: 657\n",
      "RMSE: 4.15634\n",
      "\n",
      "Iteration: 658\n",
      "RMSE: 4.15761\n",
      "\n",
      "Iteration: 659\n",
      "RMSE: 4.15692\n",
      "\n",
      "Iteration: 660\n",
      "RMSE: 4.15807\n",
      "\n",
      "Iteration: 661\n",
      "RMSE: 4.16184\n",
      "\n",
      "Iteration: 662\n",
      "RMSE: 4.15858\n",
      "\n",
      "Iteration: 663\n",
      "RMSE: 4.16103\n",
      "\n",
      "Iteration: 664\n",
      "RMSE: 4.15995\n",
      "\n",
      "Iteration: 665\n",
      "RMSE: 4.15981\n",
      "\n",
      "Iteration: 666\n",
      "RMSE: 4.1576\n",
      "\n",
      "Iteration: 667\n",
      "RMSE: 4.15777\n",
      "\n",
      "Iteration: 668\n",
      "RMSE: 4.15947\n",
      "\n",
      "Iteration: 669\n",
      "RMSE: 4.1592\n",
      "\n",
      "Iteration: 670\n",
      "RMSE: 4.15904\n",
      "\n",
      "Iteration: 671\n",
      "RMSE: 4.1585\n",
      "\n",
      "Iteration: 672\n",
      "RMSE: 4.1585\n",
      "\n",
      "Iteration: 673\n",
      "RMSE: 4.15837\n",
      "\n",
      "Iteration: 674\n",
      "RMSE: 4.15709\n",
      "\n",
      "Iteration: 675\n",
      "RMSE: 4.15779\n",
      "\n",
      "Iteration: 676\n",
      "RMSE: 4.15935\n",
      "\n",
      "Iteration: 677\n",
      "RMSE: 4.15877\n",
      "\n",
      "Iteration: 678\n",
      "RMSE: 4.15883\n",
      "\n",
      "Iteration: 679\n",
      "RMSE: 4.15922\n",
      "\n",
      "Iteration: 680\n",
      "RMSE: 4.15867\n",
      "\n",
      "Iteration: 681\n",
      "RMSE: 4.15815\n",
      "\n",
      "Iteration: 682\n",
      "RMSE: 4.15678\n",
      "\n",
      "Iteration: 683\n",
      "RMSE: 4.1566\n",
      "\n",
      "Iteration: 684\n",
      "RMSE: 4.15598\n",
      "\n",
      "Iteration: 685\n",
      "RMSE: 4.15618\n",
      "\n",
      "Iteration: 686\n",
      "RMSE: 4.15449\n",
      "\n",
      "Iteration: 687\n",
      "RMSE: 4.15927\n",
      "\n",
      "Iteration: 688\n",
      "RMSE: 4.15882\n",
      "\n",
      "Iteration: 689\n",
      "RMSE: 4.15921\n",
      "\n",
      "Iteration: 690\n",
      "RMSE: 4.15909\n",
      "\n",
      "Iteration: 691\n",
      "RMSE: 4.15761\n",
      "\n",
      "Iteration: 692\n",
      "RMSE: 4.15742\n",
      "\n",
      "Iteration: 693\n",
      "RMSE: 4.15599\n",
      "\n",
      "Iteration: 694\n",
      "RMSE: 4.15684\n",
      "\n",
      "Iteration: 695\n",
      "RMSE: 4.15769\n",
      "\n",
      "Iteration: 696\n",
      "RMSE: 4.15657\n",
      "\n",
      "Iteration: 697\n",
      "RMSE: 4.15524\n",
      "\n",
      "Iteration: 698\n",
      "RMSE: 4.15687\n",
      "\n",
      "Iteration: 699\n",
      "RMSE: 4.1581\n",
      "\n",
      "Iteration: 700\n",
      "RMSE: 4.15827\n",
      "\n",
      "Iteration: 701\n",
      "RMSE: 4.15746\n",
      "\n",
      "Iteration: 702\n",
      "RMSE: 4.15712\n",
      "\n",
      "Iteration: 703\n",
      "RMSE: 4.15504\n",
      "\n",
      "Iteration: 704\n",
      "RMSE: 4.15773\n",
      "\n",
      "Iteration: 705\n",
      "RMSE: 4.159\n",
      "\n",
      "Iteration: 706\n",
      "RMSE: 4.15919\n",
      "\n",
      "Iteration: 707\n",
      "RMSE: 4.15864\n",
      "\n",
      "Iteration: 708\n",
      "RMSE: 4.15756\n",
      "\n",
      "Iteration: 709\n",
      "RMSE: 4.15506\n",
      "\n",
      "Iteration: 710\n",
      "RMSE: 4.15699\n",
      "\n",
      "Iteration: 711\n",
      "RMSE: 4.15752\n",
      "\n",
      "Iteration: 712\n",
      "RMSE: 4.15788\n",
      "\n",
      "Iteration: 713\n",
      "RMSE: 4.15727\n",
      "\n",
      "Iteration: 714\n",
      "RMSE: 4.15913\n",
      "\n",
      "Iteration: 715\n",
      "RMSE: 4.15857\n",
      "\n",
      "Iteration: 716\n",
      "RMSE: 4.15899\n",
      "\n",
      "Iteration: 717\n",
      "RMSE: 4.15628\n",
      "\n",
      "Iteration: 718\n",
      "RMSE: 4.15863\n",
      "\n",
      "Iteration: 719\n",
      "RMSE: 4.15747\n",
      "\n",
      "Iteration: 720\n",
      "RMSE: 4.15825\n",
      "\n",
      "Iteration: 721\n",
      "RMSE: 4.15687\n",
      "\n",
      "Iteration: 722\n",
      "RMSE: 4.1563\n",
      "\n",
      "Iteration: 723\n",
      "RMSE: 4.15624\n",
      "\n",
      "Iteration: 724\n",
      "RMSE: 4.15781\n",
      "\n",
      "Iteration: 725\n",
      "RMSE: 4.15611\n",
      "\n",
      "Iteration: 726\n",
      "RMSE: 4.1586\n",
      "\n",
      "Iteration: 727\n",
      "RMSE: 4.15703\n",
      "\n",
      "Iteration: 728\n",
      "RMSE: 4.15698\n",
      "\n",
      "Iteration: 729\n",
      "RMSE: 4.15683\n",
      "\n",
      "Iteration: 730\n",
      "RMSE: 4.15752\n",
      "\n",
      "Iteration: 731\n",
      "RMSE: 4.15657\n",
      "\n",
      "Iteration: 732\n",
      "RMSE: 4.15914\n",
      "\n",
      "Iteration: 733\n",
      "RMSE: 4.16022\n",
      "\n",
      "Iteration: 734\n",
      "RMSE: 4.16061\n",
      "\n",
      "Iteration: 735\n",
      "RMSE: 4.16015\n",
      "\n",
      "Iteration: 736\n",
      "RMSE: 4.15716\n",
      "\n",
      "Iteration: 737\n",
      "RMSE: 4.16056\n",
      "\n",
      "Iteration: 738\n",
      "RMSE: 4.15791\n",
      "\n",
      "Iteration: 739\n",
      "RMSE: 4.15853\n",
      "\n",
      "Iteration: 740\n",
      "RMSE: 4.15696\n",
      "\n",
      "Iteration: 741\n",
      "RMSE: 4.15783\n",
      "\n",
      "Iteration: 742\n",
      "RMSE: 4.15702\n",
      "\n",
      "Iteration: 743\n",
      "RMSE: 4.15734\n",
      "\n",
      "Iteration: 744\n",
      "RMSE: 4.1568\n",
      "\n",
      "Iteration: 745\n",
      "RMSE: 4.15814\n",
      "\n",
      "Iteration: 746\n",
      "RMSE: 4.15754\n",
      "\n",
      "Iteration: 747\n",
      "RMSE: 4.15596\n",
      "\n",
      "Iteration: 748\n",
      "RMSE: 4.15875\n",
      "\n",
      "Iteration: 749\n",
      "RMSE: 4.15772\n",
      "\n",
      "Iteration: 750\n",
      "RMSE: 4.15802\n",
      "\n",
      "Iteration: 751\n",
      "RMSE: 4.15765\n",
      "\n",
      "Iteration: 752\n",
      "RMSE: 4.15695\n",
      "\n",
      "Iteration: 753\n",
      "RMSE: 4.15986\n",
      "\n",
      "Iteration: 754\n",
      "RMSE: 4.15844\n",
      "\n",
      "Iteration: 755\n",
      "RMSE: 4.15867\n",
      "\n",
      "Iteration: 756\n",
      "RMSE: 4.15851\n",
      "\n",
      "Iteration: 757\n",
      "RMSE: 4.15696\n",
      "\n",
      "Iteration: 758\n",
      "RMSE: 4.15604\n",
      "\n",
      "Iteration: 759\n",
      "RMSE: 4.15601\n",
      "\n",
      "Iteration: 760\n",
      "RMSE: 4.15818\n",
      "\n",
      "Iteration: 761\n",
      "RMSE: 4.15847\n",
      "\n",
      "Iteration: 762\n",
      "RMSE: 4.15796\n",
      "\n",
      "Iteration: 763\n",
      "RMSE: 4.15887\n",
      "\n",
      "Iteration: 764\n",
      "RMSE: 4.15793\n",
      "\n",
      "Iteration: 765\n",
      "RMSE: 4.15877\n",
      "\n",
      "Iteration: 766\n",
      "RMSE: 4.15808\n",
      "\n",
      "Iteration: 767\n",
      "RMSE: 4.15952\n",
      "\n",
      "Iteration: 768\n",
      "RMSE: 4.15749\n",
      "\n",
      "Iteration: 769\n",
      "RMSE: 4.15667\n",
      "\n",
      "Iteration: 770\n",
      "RMSE: 4.15812\n",
      "\n",
      "Iteration: 771\n",
      "RMSE: 4.15867\n",
      "\n",
      "Iteration: 772\n",
      "RMSE: 4.15655\n",
      "\n",
      "Iteration: 773\n",
      "RMSE: 4.15763\n",
      "\n",
      "Iteration: 774\n",
      "RMSE: 4.15908\n",
      "\n",
      "Iteration: 775\n",
      "RMSE: 4.15774\n",
      "\n",
      "Iteration: 776\n",
      "RMSE: 4.15607\n",
      "\n",
      "Iteration: 777\n",
      "RMSE: 4.1559\n",
      "\n",
      "Iteration: 778\n",
      "RMSE: 4.15557\n",
      "\n",
      "Iteration: 779\n",
      "RMSE: 4.15565\n",
      "\n",
      "Iteration: 780\n",
      "RMSE: 4.15667\n",
      "\n",
      "Iteration: 781\n",
      "RMSE: 4.15631\n",
      "\n",
      "Iteration: 782\n",
      "RMSE: 4.1573\n",
      "\n",
      "Iteration: 783\n",
      "RMSE: 4.15513\n",
      "\n",
      "Iteration: 784\n",
      "RMSE: 4.15728\n",
      "\n",
      "Iteration: 785\n",
      "RMSE: 4.15477\n",
      "\n",
      "Iteration: 786\n",
      "RMSE: 4.15596\n",
      "\n",
      "Iteration: 787\n",
      "RMSE: 4.15689\n",
      "\n",
      "Iteration: 788\n",
      "RMSE: 4.15679\n",
      "\n",
      "Iteration: 789\n",
      "RMSE: 4.15816\n",
      "\n",
      "Iteration: 790\n",
      "RMSE: 4.15667\n",
      "\n",
      "Iteration: 791\n",
      "RMSE: 4.15663\n",
      "\n",
      "Iteration: 792\n",
      "RMSE: 4.15647\n",
      "\n",
      "Iteration: 793\n",
      "RMSE: 4.15827\n",
      "\n",
      "Iteration: 794\n",
      "RMSE: 4.15685\n",
      "\n",
      "Iteration: 795\n",
      "RMSE: 4.15613\n",
      "\n",
      "Iteration: 796\n",
      "RMSE: 4.15649\n",
      "\n",
      "Iteration: 797\n",
      "RMSE: 4.1563\n",
      "\n",
      "Iteration: 798\n",
      "RMSE: 4.15712\n",
      "\n",
      "Iteration: 799\n",
      "RMSE: 4.15812\n",
      "\n",
      "Iteration: 800\n",
      "RMSE: 4.1572\n",
      "\n",
      "Iteration: 801\n",
      "RMSE: 4.15575\n",
      "\n",
      "Iteration: 802\n",
      "RMSE: 4.15595\n",
      "\n",
      "Iteration: 803\n",
      "RMSE: 4.15698\n",
      "\n",
      "Iteration: 804\n",
      "RMSE: 4.15932\n",
      "\n",
      "Iteration: 805\n",
      "RMSE: 4.15982\n",
      "\n",
      "Iteration: 806\n",
      "RMSE: 4.1565\n",
      "\n",
      "Iteration: 807\n",
      "RMSE: 4.15554\n",
      "\n",
      "Iteration: 808\n",
      "RMSE: 4.15535\n",
      "\n",
      "Iteration: 809\n",
      "RMSE: 4.15631\n",
      "\n",
      "Iteration: 810\n",
      "RMSE: 4.15458\n",
      "\n",
      "Iteration: 811\n",
      "RMSE: 4.15689\n",
      "\n",
      "Iteration: 812\n",
      "RMSE: 4.15488\n",
      "\n",
      "Iteration: 813\n",
      "RMSE: 4.15619\n",
      "\n",
      "Iteration: 814\n",
      "RMSE: 4.15715\n",
      "\n",
      "Iteration: 815\n",
      "RMSE: 4.15415\n",
      "\n",
      "Iteration: 816\n",
      "RMSE: 4.1535\n",
      "\n",
      "Iteration: 817\n",
      "RMSE: 4.15597\n",
      "\n",
      "Iteration: 818\n",
      "RMSE: 4.15546\n",
      "\n",
      "Iteration: 819\n",
      "RMSE: 4.15563\n",
      "\n",
      "Iteration: 820\n",
      "RMSE: 4.15337\n",
      "\n",
      "Iteration: 821\n",
      "RMSE: 4.15443\n",
      "\n",
      "Iteration: 822\n",
      "RMSE: 4.15354\n",
      "\n",
      "Iteration: 823\n",
      "RMSE: 4.15319\n",
      "\n",
      "Iteration: 824\n",
      "RMSE: 4.15386\n",
      "\n",
      "Iteration: 825\n",
      "RMSE: 4.15305\n",
      "\n",
      "Iteration: 826\n",
      "RMSE: 4.1542\n",
      "\n",
      "Iteration: 827\n",
      "RMSE: 4.15446\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 828\n",
      "RMSE: 4.15537\n",
      "\n",
      "Iteration: 829\n",
      "RMSE: 4.15485\n",
      "\n",
      "Iteration: 830\n",
      "RMSE: 4.15455\n",
      "\n",
      "Iteration: 831\n",
      "RMSE: 4.15381\n",
      "\n",
      "Iteration: 832\n",
      "RMSE: 4.15293\n",
      "\n",
      "Iteration: 833\n",
      "RMSE: 4.15339\n",
      "\n",
      "Iteration: 834\n",
      "RMSE: 4.15438\n",
      "\n",
      "Iteration: 835\n",
      "RMSE: 4.15388\n",
      "\n",
      "Iteration: 836\n",
      "RMSE: 4.15402\n",
      "\n",
      "Iteration: 837\n",
      "RMSE: 4.15334\n",
      "\n",
      "Iteration: 838\n",
      "RMSE: 4.1554\n",
      "\n",
      "Iteration: 839\n",
      "RMSE: 4.15568\n",
      "\n",
      "Iteration: 840\n",
      "RMSE: 4.15788\n",
      "\n",
      "Iteration: 841\n",
      "RMSE: 4.15639\n",
      "\n",
      "Iteration: 842\n",
      "RMSE: 4.15776\n",
      "\n",
      "Iteration: 843\n",
      "RMSE: 4.15681\n",
      "\n",
      "Iteration: 844\n",
      "RMSE: 4.15712\n",
      "\n",
      "Iteration: 845\n",
      "RMSE: 4.15679\n",
      "\n",
      "Iteration: 846\n",
      "RMSE: 4.15642\n",
      "\n",
      "Iteration: 847\n",
      "RMSE: 4.15971\n",
      "\n",
      "Iteration: 848\n",
      "RMSE: 4.15703\n",
      "\n",
      "Iteration: 849\n",
      "RMSE: 4.15466\n",
      "\n",
      "Iteration: 850\n",
      "RMSE: 4.15552\n",
      "\n",
      "Iteration: 851\n",
      "RMSE: 4.15658\n",
      "\n",
      "Iteration: 852\n",
      "RMSE: 4.15462\n",
      "\n",
      "Iteration: 853\n",
      "RMSE: 4.1566\n",
      "\n",
      "Iteration: 854\n",
      "RMSE: 4.15421\n",
      "\n",
      "Iteration: 855\n",
      "RMSE: 4.15498\n",
      "\n",
      "Iteration: 856\n",
      "RMSE: 4.15379\n",
      "\n",
      "Iteration: 857\n",
      "RMSE: 4.15441\n",
      "\n",
      "Iteration: 858\n",
      "RMSE: 4.15279\n",
      "\n",
      "Iteration: 859\n",
      "RMSE: 4.15556\n",
      "\n",
      "Iteration: 860\n",
      "RMSE: 4.15473\n",
      "\n",
      "Iteration: 861\n",
      "RMSE: 4.15602\n",
      "\n",
      "Iteration: 862\n",
      "RMSE: 4.15379\n",
      "\n",
      "Iteration: 863\n",
      "RMSE: 4.15428\n",
      "\n",
      "Iteration: 864\n",
      "RMSE: 4.15354\n",
      "\n",
      "Iteration: 865\n",
      "RMSE: 4.1558\n",
      "\n",
      "Iteration: 866\n",
      "RMSE: 4.15519\n",
      "\n",
      "Iteration: 867\n",
      "RMSE: 4.15477\n",
      "\n",
      "Iteration: 868\n",
      "RMSE: 4.15636\n",
      "\n",
      "Iteration: 869\n",
      "RMSE: 4.15373\n",
      "\n",
      "Iteration: 870\n",
      "RMSE: 4.15472\n",
      "\n",
      "Iteration: 871\n",
      "RMSE: 4.15732\n",
      "\n",
      "Iteration: 872\n",
      "RMSE: 4.15654\n",
      "\n",
      "Iteration: 873\n",
      "RMSE: 4.15646\n",
      "\n",
      "Iteration: 874\n",
      "RMSE: 4.15549\n",
      "\n",
      "Iteration: 875\n",
      "RMSE: 4.15704\n",
      "\n",
      "Iteration: 876\n",
      "RMSE: 4.15463\n",
      "\n",
      "Iteration: 877\n",
      "RMSE: 4.15368\n",
      "\n",
      "Iteration: 878\n",
      "RMSE: 4.15772\n",
      "\n",
      "Iteration: 879\n",
      "RMSE: 4.15647\n",
      "\n",
      "Iteration: 880\n",
      "RMSE: 4.15665\n",
      "\n",
      "Iteration: 881\n",
      "RMSE: 4.15569\n",
      "\n",
      "Iteration: 882\n",
      "RMSE: 4.15439\n",
      "\n",
      "Iteration: 883\n",
      "RMSE: 4.1527\n",
      "\n",
      "Iteration: 884\n",
      "RMSE: 4.1554\n",
      "\n",
      "Iteration: 885\n",
      "RMSE: 4.15438\n",
      "\n",
      "Iteration: 886\n",
      "RMSE: 4.15238\n",
      "\n",
      "Iteration: 887\n",
      "RMSE: 4.15265\n",
      "\n",
      "Iteration: 888\n",
      "RMSE: 4.1552\n",
      "\n",
      "Iteration: 889\n",
      "RMSE: 4.15408\n",
      "\n",
      "Iteration: 890\n",
      "RMSE: 4.15447\n",
      "\n",
      "Iteration: 891\n",
      "RMSE: 4.15393\n",
      "\n",
      "Iteration: 892\n",
      "RMSE: 4.15473\n",
      "\n",
      "Iteration: 893\n",
      "RMSE: 4.15443\n",
      "\n",
      "Iteration: 894\n",
      "RMSE: 4.15489\n",
      "\n",
      "Iteration: 895\n",
      "RMSE: 4.15547\n",
      "\n",
      "Iteration: 896\n",
      "RMSE: 4.15547\n",
      "\n",
      "Iteration: 897\n",
      "RMSE: 4.15386\n",
      "\n",
      "Iteration: 898\n",
      "RMSE: 4.15405\n",
      "\n",
      "Iteration: 899\n",
      "RMSE: 4.15272\n",
      "\n",
      "Iteration: 900\n",
      "RMSE: 4.15296\n",
      "\n",
      "Iteration: 901\n",
      "RMSE: 4.15311\n",
      "\n",
      "Iteration: 902\n",
      "RMSE: 4.15507\n",
      "\n",
      "Iteration: 903\n",
      "RMSE: 4.15346\n",
      "\n",
      "Iteration: 904\n",
      "RMSE: 4.15461\n",
      "\n",
      "Iteration: 905\n",
      "RMSE: 4.15206\n",
      "\n",
      "Iteration: 906\n",
      "RMSE: 4.15446\n",
      "\n",
      "Iteration: 907\n",
      "RMSE: 4.15504\n",
      "\n",
      "Iteration: 908\n",
      "RMSE: 4.15574\n",
      "\n",
      "Iteration: 909\n",
      "RMSE: 4.15402\n",
      "\n",
      "Iteration: 910\n",
      "RMSE: 4.15308\n",
      "\n",
      "Iteration: 911\n",
      "RMSE: 4.155\n",
      "\n",
      "Iteration: 912\n",
      "RMSE: 4.15647\n",
      "\n",
      "Iteration: 913\n",
      "RMSE: 4.15674\n",
      "\n",
      "Iteration: 914\n",
      "RMSE: 4.15459\n",
      "\n",
      "Iteration: 915\n",
      "RMSE: 4.15744\n",
      "\n",
      "Iteration: 916\n",
      "RMSE: 4.15384\n",
      "\n",
      "Iteration: 917\n",
      "RMSE: 4.15472\n",
      "\n",
      "Iteration: 918\n",
      "RMSE: 4.15455\n",
      "\n",
      "Iteration: 919\n",
      "RMSE: 4.15229\n",
      "\n",
      "Iteration: 920\n",
      "RMSE: 4.15317\n",
      "\n",
      "Iteration: 921\n",
      "RMSE: 4.15333\n",
      "\n",
      "Iteration: 922\n",
      "RMSE: 4.15408\n",
      "\n",
      "Iteration: 923\n",
      "RMSE: 4.15353\n",
      "\n",
      "Iteration: 924\n",
      "RMSE: 4.15217\n",
      "\n",
      "Iteration: 925\n",
      "RMSE: 4.15339\n",
      "\n",
      "Iteration: 926\n",
      "RMSE: 4.15074\n",
      "\n",
      "Iteration: 927\n",
      "RMSE: 4.15465\n",
      "\n",
      "Iteration: 928\n",
      "RMSE: 4.15373\n",
      "\n",
      "Iteration: 929\n",
      "RMSE: 4.15498\n",
      "\n",
      "Iteration: 930\n",
      "RMSE: 4.1556\n",
      "\n",
      "Iteration: 931\n",
      "RMSE: 4.15304\n",
      "\n",
      "Iteration: 932\n",
      "RMSE: 4.15465\n",
      "\n",
      "Iteration: 933\n",
      "RMSE: 4.15367\n",
      "\n",
      "Iteration: 934\n",
      "RMSE: 4.15473\n",
      "\n",
      "Iteration: 935\n",
      "RMSE: 4.15471\n",
      "\n",
      "Iteration: 936\n",
      "RMSE: 4.15567\n",
      "\n",
      "Iteration: 937\n",
      "RMSE: 4.1553\n",
      "\n",
      "Iteration: 938\n",
      "RMSE: 4.15612\n",
      "\n",
      "Iteration: 939\n",
      "RMSE: 4.15595\n",
      "\n",
      "Iteration: 940\n",
      "RMSE: 4.15551\n",
      "\n",
      "Iteration: 941\n",
      "RMSE: 4.15551\n",
      "\n",
      "Iteration: 942\n",
      "RMSE: 4.15364\n",
      "\n",
      "Iteration: 943\n",
      "RMSE: 4.1547\n",
      "\n",
      "Iteration: 944\n",
      "RMSE: 4.1545\n",
      "\n",
      "Iteration: 945\n",
      "RMSE: 4.15482\n",
      "\n",
      "Iteration: 946\n",
      "RMSE: 4.15417\n",
      "\n",
      "Iteration: 947\n",
      "RMSE: 4.15322\n",
      "\n",
      "Iteration: 948\n",
      "RMSE: 4.15297\n",
      "\n",
      "Iteration: 949\n",
      "RMSE: 4.154\n",
      "\n",
      "Iteration: 950\n",
      "RMSE: 4.15177\n",
      "\n",
      "Iteration: 951\n",
      "RMSE: 4.15395\n",
      "\n",
      "Iteration: 952\n",
      "RMSE: 4.15337\n",
      "\n",
      "Iteration: 953\n",
      "RMSE: 4.15431\n",
      "\n",
      "Iteration: 954\n",
      "RMSE: 4.15226\n",
      "\n",
      "Iteration: 955\n",
      "RMSE: 4.15305\n",
      "\n",
      "Iteration: 956\n",
      "RMSE: 4.15527\n",
      "\n",
      "Iteration: 957\n",
      "RMSE: 4.15138\n",
      "\n",
      "Iteration: 958\n",
      "RMSE: 4.15376\n",
      "\n",
      "Iteration: 959\n",
      "RMSE: 4.15315\n",
      "\n",
      "Iteration: 960\n",
      "RMSE: 4.15528\n",
      "\n",
      "Iteration: 961\n",
      "RMSE: 4.15594\n",
      "\n",
      "Iteration: 962\n",
      "RMSE: 4.15606\n",
      "\n",
      "Iteration: 963\n",
      "RMSE: 4.15597\n",
      "\n",
      "Iteration: 964\n",
      "RMSE: 4.15667\n",
      "\n",
      "Iteration: 965\n",
      "RMSE: 4.15627\n",
      "\n",
      "Iteration: 966\n",
      "RMSE: 4.15389\n",
      "\n",
      "Iteration: 967\n",
      "RMSE: 4.15359\n",
      "\n",
      "Iteration: 968\n",
      "RMSE: 4.15297\n",
      "\n",
      "Iteration: 969\n",
      "RMSE: 4.15342\n",
      "\n",
      "Iteration: 970\n",
      "RMSE: 4.15471\n",
      "\n",
      "Iteration: 971\n",
      "RMSE: 4.15533\n",
      "\n",
      "Iteration: 972\n",
      "RMSE: 4.15454\n",
      "\n",
      "Iteration: 973\n",
      "RMSE: 4.15643\n",
      "\n",
      "Iteration: 974\n",
      "RMSE: 4.15336\n",
      "\n",
      "Iteration: 975\n",
      "RMSE: 4.15231\n",
      "\n",
      "Iteration: 976\n",
      "RMSE: 4.15104\n",
      "\n",
      "Iteration: 977\n",
      "RMSE: 4.154\n",
      "\n",
      "Iteration: 978\n",
      "RMSE: 4.15376\n",
      "\n",
      "Iteration: 979\n",
      "RMSE: 4.15413\n",
      "\n",
      "Iteration: 980\n",
      "RMSE: 4.15162\n",
      "\n",
      "Iteration: 981\n",
      "RMSE: 4.15275\n",
      "\n",
      "Iteration: 982\n",
      "RMSE: 4.15388\n",
      "\n",
      "Iteration: 983\n",
      "RMSE: 4.15513\n",
      "\n",
      "Iteration: 984\n",
      "RMSE: 4.15584\n",
      "\n",
      "Iteration: 985\n",
      "RMSE: 4.15474\n",
      "\n",
      "Iteration: 986\n",
      "RMSE: 4.15343\n",
      "\n",
      "Iteration: 987\n",
      "RMSE: 4.15481\n",
      "\n",
      "Iteration: 988\n",
      "RMSE: 4.15436\n",
      "\n",
      "Iteration: 989\n",
      "RMSE: 4.15307\n",
      "\n",
      "Iteration: 990\n",
      "RMSE: 4.15283\n",
      "\n",
      "Iteration: 991\n",
      "RMSE: 4.15265\n",
      "\n",
      "Iteration: 992\n",
      "RMSE: 4.1551\n",
      "\n",
      "Iteration: 993\n",
      "RMSE: 4.15512\n",
      "\n",
      "Iteration: 994\n",
      "RMSE: 4.15345\n",
      "\n",
      "Iteration: 995\n",
      "RMSE: 4.15506\n",
      "\n",
      "Iteration: 996\n",
      "RMSE: 4.15246\n",
      "\n",
      "Iteration: 997\n",
      "RMSE: 4.15427\n",
      "\n",
      "Iteration: 998\n",
      "RMSE: 4.15387\n",
      "\n",
      "Iteration: 999\n",
      "RMSE: 4.15278\n",
      "\n",
      "Iteration: 1000\n",
      "RMSE: 4.15219\n",
      "\n",
      "8064\n",
      "8070\n",
      "8076\n",
      "8082\n",
      "8088\n",
      "8094\n",
      "8100\n",
      "8106\n",
      "8112\n",
      "8118\n",
      "8124\n",
      "8130\n",
      "8136\n",
      "8142\n",
      "8148\n",
      "8154\n",
      "8160\n",
      "8166\n",
      "8172\n",
      "8178\n",
      "8184\n",
      "8190\n",
      "8196\n",
      "8202\n",
      "8208\n",
      "8214\n",
      "8220\n",
      "8226\n",
      "8232\n",
      "8238\n",
      "8244\n",
      "8250\n",
      "8256\n",
      "8262\n",
      "8268\n",
      "8274\n",
      "8280\n",
      "8286\n",
      "8292\n",
      "8298\n",
      "8304\n",
      "8310\n",
      "8316\n",
      "8322\n",
      "8328\n",
      "8334\n",
      "8340\n",
      "8346\n",
      "8352\n",
      "8358\n",
      "8364\n",
      "8370\n",
      "8376\n",
      "8382\n",
      "8388\n",
      "8394\n",
      "8400\n",
      "8406\n",
      "8412\n",
      "8418\n",
      "8424\n",
      "8430\n",
      "8436\n",
      "8442\n",
      "8448\n",
      "8454\n",
      "8460\n",
      "8466\n",
      "8472\n",
      "8478\n",
      "8484\n",
      "8490\n",
      "8496\n",
      "8502\n",
      "8508\n",
      "8514\n",
      "8520\n",
      "8526\n",
      "8532\n",
      "8538\n",
      "8544\n",
      "8550\n",
      "8556\n",
      "8562\n",
      "8568\n",
      "8574\n",
      "8580\n",
      "8586\n",
      "8592\n",
      "8598\n",
      "8604\n",
      "8610\n",
      "8616\n",
      "8622\n",
      "8628\n",
      "8634\n",
      "8640\n",
      "8646\n",
      "8652\n",
      "8658\n",
      "8664\n",
      "8670\n",
      "8676\n",
      "8682\n",
      "8688\n",
      "8694\n",
      "8700\n",
      "8706\n",
      "8712\n",
      "8718\n",
      "8724\n",
      "8730\n",
      "8736\n",
      "8742\n",
      "8748\n",
      "8754\n",
      "8760\n",
      "8766\n",
      "8772\n",
      "8778\n",
      "Final MAPE: 0.164031\n",
      "Final RMSE: 6.08458\n",
      "\n",
      "Running time: 32810 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 144])\n",
    "num_step = 6\n",
    "num_roll = int(144 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 1000\n",
    "gibbs_iter = 100\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat_hat10 = np.percentile(result, 5, axis = 2)\n",
    "mat_hat90 = np.percentile(result, 95, axis = 2)\n",
    "mat_hat = np.mean(result, axis = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = dense_mat.copy()\n",
    "pred_steps = int(num_roll * num_step)\n",
    "tv = 144"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "figsize = 2\n",
    "for i in range(3):\n",
    "    fig = plt.figure(figsize = (4 * figsize, 1 * figsize))\n",
    "    ax = fig.add_axes([0.13, 0.28, 0.85, 0.68])\n",
    "    plt.plot(X[i, 54 * tv :], color = \"black\", linewidth = 0.5)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 54 * tv, X.shape[1] - 54 * tv)), \n",
    "             mat_hat[i, :], color = \"#e3120b\", linewidth = 2.0)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 54 * tv, X.shape[1] - 54 * tv)), \n",
    "             mat_hat10[i, :], color = \"blue\", linewidth = 0.5)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 54 * tv, X.shape[1] - 54 * tv)), \n",
    "             mat_hat90[i, :], color = \"green\", linewidth = 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "\n",
    "tensor = scipy.io.loadmat('../datasets/Hangzhou-data-set/tensor.mat')\n",
    "tensor = tensor['tensor']\n",
    "random_matrix = scipy.io.loadmat('../datasets/Hangzhou-data-set/random_matrix.mat')\n",
    "random_matrix = random_matrix['random_matrix']\n",
    "random_tensor = scipy.io.loadmat('../datasets/Hangzhou-data-set/random_tensor.mat')\n",
    "random_tensor = random_tensor['random_tensor']\n",
    "\n",
    "dense_mat = tensor.reshape([tensor.shape[0], tensor.shape[1] * tensor.shape[2]])\n",
    "missing_rate = 0.4\n",
    "\n",
    "# =============================================================================\n",
    "### Random missing (RM) scenario\n",
    "### Set the RM scenario by:\n",
    "binary_mat = np.round(random_tensor + 0.5 - missing_rate).reshape([random_tensor.shape[0], \n",
    "                                                                   random_tensor.shape[1] \n",
    "                                                                   * random_tensor.shape[2]])\n",
    "# =============================================================================\n",
    "\n",
    "sparse_mat = np.multiply(dense_mat, binary_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: 101.287\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: 70.3381\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: 53.6979\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: 49.4189\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: 47.1461\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: 45.86\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: 45.7183\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: 45.8896\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: 46.2484\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: 46.7664\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: 47.4777\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: 47.3682\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: 47.5301\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: 46.6131\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: 45.4952\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: 44.8379\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: 44.3899\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: 44.7274\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: 45.0761\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: 45.8206\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: 45.0064\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: 44.4442\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: 45.485\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: 45.1824\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: 44.531\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: 44.591\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: 44.6757\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: 44.9708\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: 45.0923\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: 45.0159\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: 44.904\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: 45.3887\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: 46.0251\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: 45.6158\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: 45.502\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: 44.7124\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: 44.7735\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: 43.9153\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: 43.7807\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: 44.1097\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: 43.6194\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: 44.0903\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: 44.4178\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: 43.6577\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: 43.8949\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: 44.4267\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: 43.694\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: 43.6536\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: 44.7691\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: 43.8228\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: 44.2445\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: 43.9087\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: 43.3626\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: 43.486\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: 43.7106\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: 44.1793\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: 43.8947\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: 44.2573\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: 44.0629\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: 43.4897\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: 42.5123\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: 42.6549\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: 43.0575\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: 43.3994\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: 42.6277\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: 43.9714\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: 43.942\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: 43.5723\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: 44.0702\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: 43.9521\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: 44.324\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: 44.3996\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: 44.9953\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: 43.1493\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: 43.4973\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: 43.2437\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: 43.317\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: 42.9942\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: 42.1611\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: 42.6557\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: 42.1078\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: 42.2983\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: 43.1372\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: 42.7722\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: 43.1752\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: 42.8701\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: 43.3126\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: 42.5251\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: 42.6926\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: 42.7488\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: 42.4678\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: 42.4275\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: 43.4612\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: 43.1562\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: 42.5489\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: 42.4343\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: 41.5781\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: 42.5625\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: 43.1908\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: 43.0127\n",
      "\n",
      "2160\n",
      "2165\n",
      "2170\n",
      "2175\n",
      "2180\n",
      "2185\n",
      "2190\n",
      "2195\n",
      "2200\n",
      "2205\n",
      "2210\n",
      "2215\n",
      "2220\n",
      "2225\n",
      "2230\n",
      "2235\n",
      "2240\n",
      "2245\n",
      "2250\n",
      "2255\n",
      "2260\n",
      "2265\n",
      "2270\n",
      "2275\n",
      "2280\n",
      "2285\n",
      "2290\n",
      "2295\n",
      "2300\n",
      "2305\n",
      "2310\n",
      "2315\n",
      "2320\n",
      "2325\n",
      "2330\n",
      "2335\n",
      "2340\n",
      "2345\n",
      "2350\n",
      "2355\n",
      "2360\n",
      "2365\n",
      "2370\n",
      "2375\n",
      "2380\n",
      "2385\n",
      "2390\n",
      "2395\n",
      "2400\n",
      "2405\n",
      "2410\n",
      "2415\n",
      "2420\n",
      "2425\n",
      "2430\n",
      "2435\n",
      "2440\n",
      "2445\n",
      "2450\n",
      "2455\n",
      "2460\n",
      "2465\n",
      "2470\n",
      "2475\n",
      "2480\n",
      "2485\n",
      "2490\n",
      "2495\n",
      "2500\n",
      "2505\n",
      "2510\n",
      "2515\n",
      "2520\n",
      "2525\n",
      "2530\n",
      "2535\n",
      "2540\n",
      "2545\n",
      "2550\n",
      "2555\n",
      "2560\n",
      "2565\n",
      "2570\n",
      "2575\n",
      "2580\n",
      "2585\n",
      "2590\n",
      "2595\n",
      "2600\n",
      "2605\n",
      "2610\n",
      "2615\n",
      "2620\n",
      "2625\n",
      "2630\n",
      "2635\n",
      "2640\n",
      "2645\n",
      "2650\n",
      "2655\n",
      "2660\n",
      "2665\n",
      "2670\n",
      "2675\n",
      "2680\n",
      "2685\n",
      "2690\n",
      "2695\n",
      "Final MAPE: 0.585583\n",
      "Final RMSE: 80.7796\n",
      "\n",
      "Running time: 875 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 108])\n",
    "num_step = 5\n",
    "num_roll = int(108 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 100\n",
    "gibbs_iter = 10\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA/4AAADmCAYAAABs8V6mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3XuQnPV56Pnv7730vec+unMTBmMuNsRgOzdEsLLrKp+Tde2peFM2qc36+Pg4eE3ZbMXlrZPgyjoXckhWPnKcEIcE7yk7Xjs5KSXBjuOjKBaBNbYAgQBxESCBpNFopqdn+vbe3/e3f3RPz7RGBgEz09Pdz+cf6J4Z1dP99uV93uf5PT+ltdYIIYQQQgghhBCiLxndDkAIIYQQQgghhBBrRxJ/IYQQQgghhBCij0niL4QQQgghhBBC9DFJ/IUQQgghhBBCiD4mib8QQgghhBBCCNHHJPEXQgghhBBCCCH6mCT+QgghhBBCCCFEH5PEXwghhBBCCCGE6GOS+AshhBBCCCGEEH1MEn8hhBBCCCGEEKKPWd0OYNHU1FS3Q3hDJiYmKJVK3Q5DrCI5pv1Jjmt/kuPan+S49ic5rv1Jjmt/kuPae7Zt23ZBv/e6if/U1BR79uxp356ZmeHDH/4wu3btYs+ePczOzjI5OclnP/tZCoUCWmvuv/9+Dh8+TDqd5vbbb2fnzp1v/pEIIYQQQgghhBDiTXvdVv9t27Zxzz33cM899/AHf/AHpFIp3vOe97Bv3z6uu+469u7dy3XXXce+ffsAOHz4MNPT0+zdu5dPfOIT3HfffWv+IIQQQgghhBBCCHF+b2iN/1NPPcWWLVuYnJzk0KFD7Nq1C4Bdu3Zx6NAhAB599FFuvvlmlFJceeWVNBoN5ufnVz9yIYQQQgghhBBCvK43tMb/4Ycf5md/9mcBqFQqjI6OAjA6Okq1WgWgXC4zMTHR/pvx8XHK5XL7dxft37+f/fv3A3D33Xd3/E0vsCyr52IWr02OaX+S49qf5Lj2Jzmu/UmOa3+S49qf5Lj2rwtO/KMo4rHHHuMjH/nIa/6e1nrFfUqpFfft3r2b3bt3t2/32hAJGXzRf+SY9ic5rv1Jjmt/kuPan+S49ic5rv1JjmvvudDhfhfc6n/48GEuu+wyRkZGABgeHm638M/PzzM0NAQ0K/zLXyxzc3Mrqv1CCCGEEEIIIYRYHxec+C9v8we48cYbOXjwIAAHDx7kpptuat//4IMPorXmhRdeIJfLSeIvhBA/wYnqiW6HIIQQQggh+twFJf6+73PkyBHe+973tu/70Ic+xJEjR7jjjjs4cuQIH/rQhwC44YYb2LRpE3fccQd/9md/xsc//vG1iVwIIXpULajxbPlZAL7+7Ne7HI0QQgghhOh3F7TGP51O85d/+Zcd9xWLRe66664Vv6uUkmRfCCFew4nqCQ7PHOYdY++gGlS7HY4QQgghhOhzb2g7PyGEEG9dyS3hxR4AFb/S5WiEEEIIIUS/k8RfCCHW2Zw3hxu5AFLxHzAPnX6o2yEIIYQQYgBJ4i+EEOus5JYk8R9AiU44cPJAt8MQQgghxACSxF8IIdZZPaxjGRY6SajUS+gk6XZIYh14kUeYhN0OQwghhBADSBJ/IYTokuD//n3c2dPwZ3/S7VDEOnAjlyAOuh2GEEIIIQaQJP5CCNEl7je/Rmho9P33dTsUsQ7cI48SPPU4OpTkf5A9PPUwT8w+0e0whBBCDBhJ/IUQoktcS2NoBaZ8FA8C5zc+RfTS8/Ctb3Y7FNFFZa8su3kIIYRYd3K2KYQQXeJZkIkAJR/Fg8C1NIEBevpMt0MRXdQ4fRzn9PFuhyGEEGLAWN0OQAghBpFC4VqQjZCK/4DwLPAMEwyz26GILtFRhPO1P8VO0vDeX+t2OEIIIQaInG0KIcQ6ciOXjJkBwLM0+VARS+I/EFwLjrFTLvQMssCnEbt4rmzjKYQQYn3J2YcQQqyjOXeOiewEGo1rw5CvCCzV7bDEGqkGSwlewwKtLan4D7IwxLGbyz50HHc7GiHEOvn2C9/udghCSOIvhBDrac6bYywzBjQr/oY3RCCLrvrWvUfuxY1cAOqWhRmmpOI/yMKQyGgm/kjiL8TAODp3tNshCCGJvxBCrKc5b46xsoc+fQrPgrPOlYSWfBT3q6NHj1JqlAComxZGmEFJxX9whSGpGAITiMJuRyOEWCf1sN7tEISQxF8IIdaTc/x5sp+9E/5hH64FplcktOWjuF/NlGZ4pfQKAA3bwIjSUvEfECdPnuThhx/uvDMMqeohauQhjLoTmBBi3UniLzYCOfsQQoh1ouOY8P+5DysBdLPV3/SGCeSTuG8FYcCJmRMANEwDI8zIGv8BcebMGV544YXOO4OAuWSShWQMIkn8hRgUjbDR7RCEkMRfCCHWTb1GVC1jJ2DHUE0B/hCBVPz7VhiHnJ4/jdYaxzZQUQZMSfwHQbVapVQqdd4ZhsSYaBTEkvgLMQj0Y4eoHfkR+pmnux2KGHAXNFKq0Whw7733cvLkSZRS/Pqv/zrbtm1jz549zM7OMjk5yWc/+1kKhQJaa+6//34OHz5MOp3m9ttvZ+fOnWv9OIQQYuMLI0KjmfRnYkU5q6E0QpjtdmBirSRJwlRlCqKICBOtDdC622GJdVCr1c6b+CcYJBhS8ReiTz3xxBO8853vxDCaF/X1wX+hHrnw8L/CNdd2OToxyC6ozHT//fdz/fXX86UvfYl77rmH7du3s2/fPq677jr27t3Lddddx759+wA4fPgw09PT7N27l0984hPcd999a/oAhBCiZ0QRx7mIqegysiEspDU6GCIwZTu/frVZpZmvzUDgE7cTPhnqNggqlcrKO8OABFMSfyH62D/+4z8yOzu7dEcY0Uhp6fIRXfe6ib/jODz77LPceuutAFiWRT6f59ChQ+zatQuAXbt2cejQIQAeffRRbr75ZpRSXHnllTQaDebn59fwIQghxMb22GOPNf8nCplTIzzu/wzZCFxbE0ZFQun87kv6mad53/EXufzIYQgCYiwSbUIk27gNglqtxtDQUOedYUiMgZbEX4i+5bouU1NTS3eEAfWURstAT9Flr5v4z8zMMDQ0xJ/8yZ/wuc99jnvvvRfP86hUKoyOjgIwOjpKtVoFoFwuMzEx0f778fFxyuXyGoUvhBAbWxRFfO5znwPg3j/+YwJD8UJwPdlI4VoQRnmCC1p0JXrOoR8BkPc88ANibZKg0JLwDYQgCEin0513hiFaS8VfiH7meR6nT59u346igLplyntedN3rnm7Gcczx48f52Mc+xhVXXMH999/fbus/H32etYtKrWxj3b9/P/v37wfg7rvv7rhY0Assy+q5mMVrk2Pan7p9XJ9//nkmJiZoNBr4jTqhAWE8TDakmfjHBWLblNfeG9Tt43oh3Isvbv//aCHfGupmkEulKGzw2LulF47rhcrlcmitOx6Pn822Kv6KkUIBu08e6+vpp+MqlshxPb+xsTEWFhbaz80ZC2IU2ZRNsQeeLzmu/et1E//x8XHGx8e54oorAHjf+97Hvn37GB4eZn5+ntHRUebn59vtbOPj4x3DbObm5tqdAcvt3r2b3bt3t2+vGICzwU1MTPRczOK1yTHtT90+ro888gi/+qu/yt69e/mpK67kyGOnGEk8zNDGtUPCKI+nEnntvUHdPq4XQi/btm/+9ClimredWhVvg8feLb1wXC+U4ziYpsmZM2ewbZuHpx7mvaUFtLZIMFgolVB98lhfTz8dV7FEjuv52bbN9PR0+7mpOXXMoRSNRhW/B54vOa69Z9u2bRf0e6/b6j8yMsL4+Hh7rcpTTz3Fjh07uPHGGzl48CAABw8e5KabbgLgxhtv5MEHH0RrzQsvvEAulztv4i+EEIPgxRdfZPfu3Xzve9/jphtuIFKK64ynmAl24pkQxXlCafXvT8aybrez08SYGMQQyxr/QTE2NtZe7vjN575JPahhBplmq78M+hJiIASxjxVkCSK/26FsGD/84Q9ZWFjodhgD54JONz/2sY+xd+9eoihi06ZN3H777Wit2bNnDwcOHGBiYoI777wTgBtuuIHHH3+cO+64g1Qqxe23376mD0AIITayIAjIZDJ88YtfZLRYIMbgWvMpHvbfhpkcJYmzBCTdDlOsAR3FnE02s1mdJTl1klhbWFoTh/6Fbakjet5i5Wzz5s3MeXOc9KebiX9a1vhDc3mo53lks/27p+n3v/99brnlFlKpVLdDEevsyJEjvPLKK7wr9jGDLEESkOt2UBvEk08+ST6fZ2RkpNuhDJQLSvwvvfRS7r777hX333XXXSvuU0rx8Y9//K1HJoQQfWBx7snNN9+MPvRjNCZDRoUkvIh0ZJBEGQKkAtyPQt/nxfgqLgmrzE29SIJBKlYEcYjd7eDEupiYmGBubg4AL/J43j+FEWaJUSATvimXy/z1X/81n/zkJ7sdypr59re/zXXXXcfWrVu7HYpYR1prvv/975PNZrk6DjH9PGESdDusDaNWq3H27NluhzFwpOgghBBrJAxDbHtZihdHJNogTx0d5kmHJkmcJUQSgH4UeC4asJxRTr76HDEWVgJhLCd/g2J8fLyd+E/mJjkWnsEIcqjYJoy8LkfXfZ7n4fv93f78yiuvtF8DYnCk02lc122+xpMAw88TyGd/W61WY2ZmptthDBxJ/IUQYo00Gg0KhcLSHVFEgkFONdBBHjsyMWODUCr+fSnwPDQG+fJWXlh4kRiTVAKRVH0Ggtaa8fFxDhw4wBe+8AV2FHbwQjyNEeQwoxRu4HQ7xK5bTIz61ZkzZ7jqqqtkUNoAuuiii7jpppvQWhMmIQQFfC2f/YtyuRyzs7PdDmPgyEgpIYRYI47jkMstW9G3PPEPC6RCk1SiZY1/n2om/opM6TKmr32OuGFixxDEYbdDE2ssjmMMw2B4eJj3vve9TE9Po2zFrK6xPcxhhmnc0GG424F2me/7fZv4f+tb36JYLLJ7925J/AfQL/3SL2EYBk8//TSBDsHfRGj152v9zUilUkQy52TdScVfCCHWiOM45PP5pTuiEI1BSoUQp8gFNnakCKTVvy8FbjPxr4bbcMJGq+KfNKs/oq/V63Xy+TxKKW677TY0Gq01cRJjB2msMIUTNbodZtd5nteXib/WmgceeIAvf/nL/PzP/7y0+g8g0zRRqrmzS5AE4A83/ytEF0niL4QQa+R8Ff9FCs2uZydJaQil4t+XAs/DJmRBjxIaoOI0qRgiWefZ92q1GsPDS/X8odEhkiBha5InExqtir/bxQg3Bt/3+3KNf6VS4eabb2bPnj2Mjo5Sq9XaP/unE//UxchENwRJRBIMEchF37bFwcdifUniL4QQa8RxnM5tqlpTvGPDRKO4/OwIKULQkvj3o8DzUGi0VhgazNDGig0CLR0e/a5arVIsFtu3JzaNYD55lB0Ni3RoYYQZ3EgS/36t+J86dYodO3Zw1VVXtau+0Ex2Dpw80MXIxFoLwxDLWlpJrZQi0CGxP9Js+ReiiyTxF0KINfKTKv5Ba9J/iI1NAIkk/o888ki3Q1h1ob+U0LxtXmGFNkZiEsoa/75Xq9U6Ev9Lj/yQHQcO8j/88yvkvBRGmMGTxB/P8wiC/uuAWUz8zxUkAfP+fBciEuvFdd2OC/7Dw8O4cUjijxImctH3XFL5X1+S+AshxBppNBor1vjDssRfp0ipAB3LF98DDzzQ7RBWXeAttTBfXTJI+1nM2CSUqk/fq1arDA0NtW/bLx0lHyp+5pRJKlEYYRo36b9K9xvl+z7pdLrbYay6n5T4O6FDI5TZDv3s3MR/YmICN4lJ/CHp9mpZTPZHRkaYn5cLYetJEn8hhFgj56v4a/Syin+KDC6J5P19ua1PFCxP/E2ufO5ajNiUqs9raAT9kRTVarWOrTxdMyLfut6j0NhhCjeSxN/zPDKZTLfDWHULCwuMjIysuN+JHGpB7Tx/IfqF67odr+nx8XGcJEb7w/hy0Rdovu/T6TSbNm1iZmam2+EMFEn8hRBijbiu+5qt/oG2ySpXOv2hL6deh8uGlmkNCoWZmIRS9TmvBX+BP33sT7sdxqpoNBodiX+dkEKwtNbbimzcpP+G2r1R/VrxBzrW9i9yQgcncroQjVgv56v4+xoICvLZ31Kv1ykWi5L4d4Ek/kIIsUbOV/FXKAI71byJTUa5MtsPKJVKfbfWL2qtXS4aFaq6OeG9WfGXqs9yR48exXVdnNDpm+fm3MS/oULyrcRfo7AiCy+Wiv9i5a/fZbNZHMehETVIGaluhyPWkOd5HYn/5OQkHhozyMrWvS2LS6GGhoY6drwQa08SfyGEWCMr2ljPXeO/2OoviX/zpLjRH23ei1TrQsaEmqGkNwFgJQYhMQBxEnctto3koYceYnZ2Fidy+mbw4bkX/eoqpLDsocmSjybXdQci8Z+YmGBubg4ndMjZudf/gwHRbxd7YWXFf3R0FE9pbD9LIO95YGn4aaFQoF6vdzucgSKJvxBCrBGtNYax7GN22Rp/hSbQKTLKQ6PQA579J0lCtVrtdhirajHxH1VlFpJRgOZU/1a751ef+iplr9y1+DaKRqOB4zi4kds3Ff9z3/sNY6nir9AYidE3j/WtSJKkY+uzfrCi04tm8lcul2mEDXJWri8T3jdj79693Q5h1Z2b+JumSagUmdDGZ7C/5xctVvwLhULfXfDf6CTxF0KIdaLD1hp/y0ajCFut/gkGxINdCSgWi32b+A8bFSq6OejLXFbpPV0/LRO+aSZKjuPQePRhGg/9S19eBKubUUfF34xNIkn8+9LU1BTbtm3ruC+fzzcvcEUOY5kxWebRcuLEiW6HsOqWD/fTWhPEAaEB6cDAQy74wFLFP5/PS8V/nUniL4QQ66W1xj9cXOOvbbK4aBSEkvj321o/1Upgm4l/c42/GSsC3Wzxn3amcWUvdxqNRjMp+vJ/xn3qMPzLP3c7pFUX65j/5v6v7dtGIq3+/WpqaoqtW7d23JfNZttzLDbnNlMPJNkB+nKw2/I1/i8uvMjfvPA3aG2QTRJ8SfyBZuI/NDREKpUiaM3CEetDEn8hhFgv56zxD0g1K/7agHiw13sPDw9TqVS6HcaqWqz4D42ZVHSz1T+VaNzWyd+MMyOJP82Kv+u6uDaEBtAHF4BWtHJHET8Mf75909AGiR7s9/wipVRftb6fOXNmReKfy+Xaw/025TZRC3v/Nb4a+jHxX97qv+AvMO+WiDHIRjGetPoDzVb/YrF43p0vxNqSxF8IIdZLa41/bJpgGq1W/+Ya/0Fu9Y+iiJGRkf6r+C8m/hNmu9U/FWuCVieAqUzZ2gsIw7DZ7m9rIgNoXRjrF9r3IY45mVzS+YNYkgAA27b7quo3PT3Nli1bOu5bXvHflNskS3xoXhwbhMR/wS2TYJBVAXH/XN96SxqNBvl8vtthDKQLmqjyqU99ikwmg2EYmKbJ3XffTb1eZ8+ePczOzjI5OclnP/tZCoUCWmvuv/9+Dh8+TDqd5vbbb2fnzp1r/TiEEGLji5rJfawMMC3CMMWQqjTX+EeDW/0LgoCJiYm+rfinJoaJdHOgYyoBj+ZE/0KqIBV/lrY6Cy1Q0HeJP7Xm7IrTyUWd9/fhLIM3I51O4/t+30z3D8OQVKpzy77Fin+QBIxlxqgF/XWR881wXRfH6b8Ln8vX+Ff8CguNOTRGs7svkQo3NId6mqYJIFX/dXbBo1S/8IUvMDQ01L69b98+rrvuOj70oQ+xb98+9u3bx2233cbhw4eZnp5m7969HDt2jPvuu4/f+73fW5PghRCiVzxXfo4rW2v8taHANAlDm6xy0AM+3M/3fSYnJ/uq4l+v10nbFiTA+ASq1d6fSjQOmjlvjh2FHZL400yKGvU6sQ3ZkP5L/KtVtIa5ZIJQLzvt0pL4A2QyGTzP6zjH7GXnS2RyuRye56FQFO0i0850FyLbWKrVKoVCgSRJOne/6XFhGGK3PsMq9/0XLPdVfL2DDB5JMtgl/+eff563v/3t3Q5joL3pd9qhQ4fYtWsXALt27eLQoUMAPProo9x8880opbjyyitpNBrMz8+vTrRCCNFDlp8A/tdn/yvErVZ/wwDLItI2KRW0pvoPdsW/UCjg+363Q1k1Z8+eJZ9tbek1NtZczkGr1R/NdGOay4Yvwwn7r+L1RmWzWYJqFcfS5EIFSe+/FzqSv2oVhxybjWk8su3XglT8mxYT/371ty/+LYZt4LrNi3x5O089lOF+tVqNycnJvvrch+Z7f/H9XymdZMhXJFLxB+DP//zPgc4ZKP0036MXXHDF/3d/93cB+MVf/EV2795NpVJhdLQ5rGh0dLS9DVO5XGZiYqL9d+Pj45TL5fbvLtq/fz/79+8H4O677+74m15gWVbPxSxemxzT/tTN45rNZpmYmCB84nGmv/dt+HsDfuo92Jkslm0SYGISoVGMDg1hDejrr16vMz4+Tr1ev+BjtdHfr0ePHmV8dAQaDvmtS1t7pZMEX0HDbHDVU6c4u63CxM9s3MexHkZGRsg6DerKYDbeQjGbJbOBj+2FWHzvA/gKXJ1jh/Eqnl62v7dSG/o1vJqWv1+Xt/XncjkmJyc7nq9el8vlOh7LqWdOURgtkE6nUTnFJVsu4cnqk33xeN/K5/DLL7/M9u3byeVyjI+Pr3Jk3bN4/HWSEBtgJZBgklEeiVaMj42hNniHw1p8v3qex9mzZ5mYmOh4j5z7fhFr64IS/y9+8YuMjY1RqVT4nd/5nRX7ky53vis352t72r17N7t3727fLpVKFxLKhjExMdFzMYvXJse0P3XzuDqOQ6lUIrn9E5x5j48mg0LhRRG2FdHAxiQmxmB+ZgZVKHYlzm6bnp4mCIL283UhNvr79dixY2xundw5vg8013xaKkYncOyh7/Izf/pNnrkspnTLb3Qx0u5zHAe7WsUly8n4EmpzZeob+Ni+Hq11x2tZnzqFo/PsMF7B05n2so84DDf0a3g1LX+/fvGLX+S3fuu3gOaxD8OQ6elpJicnuxniqnAcB611x3EtvfAMJ4tPNtezn63hf/OvOXPpXF8c+7fyOXzy5ElGR0d56qWnuFZfu8qRdcf999/P/Pw8pVIJvWxmTYIijUeCQWl6GnXODIiNZi2+X0ulElNTU5RKpY7PxzfyvS9+stfKzZe7oEtOY2NjQHO7pZtuuokXX3yR4eHhdgv//Px8e23W+Ph4xwGcm5tbUe0XQoh+13ERNAw5m9cEJhixgbYsbDvB1xlM4tZU/95vb36zgiBYMQyr1509e5ZcplXdNU344L+FXb+ARUSiFbMzL7GjqnAtaXMEsKOIQKeJMdtDMHuV53nt4V4A1Ko45NlhnsQlt3T/gLb6nzp1quN2P7X6T01NdWzlp4+/jPuD7+Hu+f3mHT/6IZm77sJ95ViXItw4qtUqk5OT3H/s/m6HsmqOHj3a7oCmujzxN5ut/hg9//n2ZlWrVVzXJUkSGejXRa+b+Hue116X5HkeR44c4eKLL+bGG2/k4MGDABw8eJCbbroJgBtvvJEHH3wQrTUvvPACuVxOEn8hxMDpmFIdxzRsTTUFRmJiZTKk7BifTLPVXw/2cL9+TPyr1WpzuB+AoVAXX4K65lpMIyHBIHYapBJFsrE7Ptfc4klgKgzxaSX+YdjtsN4Sx3E6t6qqVnF0rl3xbxvQxP/06dMdtzOZTPs8s9dVq1WGh4eX7pidwbE0XqXV/eE4zQGvrst0Y7AH/NVqNTZv3kzZLffNOu8tW7Zw9913N29Uq7g6y1y4jcCgOdwPNbCJf71eZ3R0lNnZ2Y68UC4CrK/XbfWvVCr84R/+IQBxHPNzP/dzXH/99Vx++eXs2bOHAwcOMDExwZ133gnADTfcwOOPP84dd9xBKpXi9ttvX9tHIIQQG5DjOORyzeqen4TgD1HJhJhxM/G3rRhfpzBVLMP9gqBvtvLqsJjYGSaGoVGKduJPQ/bxhqXquB2FBKSJMSDq7cS/Xq93JP66VsXXWTYbZ3B0HqU0WquBTfxnZmY6Jp+n0+mlKmmPW9Ht4fu4Nri6NcBu8aJWHPGx73+M73zoOwOb+FSrVbZv307drREkAWmzz74DKhWqehjXuZT6pqlWxb/3O5rerGq1ys6dO3nuuec6ZjrYto3v+xyrHePaif5Y8rGRvW7iv3nzZu65554V9xeLRe66664V9yul+PjHP7460QkhRI9anvjXjIBUbZJq+jRGYmKm03DFJQSn8lhDw81W/2hwE3/f9/uu4g8sS/wNikVNECgMIyFSCrMx2NP8/+qv/oqPfOQjNBoNcrkcdhgS6HTzxLjHK/6NRqOz4u/7aCCjPKrJMBYhIamBTfyr1Sqe57UT/35q9fc8j5GRkaU7Ap+XjB1UFy/shgEAh/2XyY1MUA2qDKeHz/Mv9T/HcdiuE+ynH8Wr/hnpj9/R7ZDekhVdC9UKHhlsr0A9E7aG+w1ud1+9Xmfnzp0cPXqUd73rXe37C4UCjUaDvzn2N5L4r4MBbzIUQoi1MV2Zxks3T2arRohR20IlrTFiAyuTJfipawl/+laMiVE0BkkUdDni7unHVn+gI/EfHk5IpTSWqTk56nPZ2aXktl/aXN+IxS2AF9viU1GIr9PE2uqLxL9QKCzd0Ur6sumYmh7CpvX4BjDxd12XoaEhXNdtv+77LfHvrPgHRHGGWqKblf3Wa3ssyfArb/8VZt3ZLkXafUmScPE/fQfXiPG++uVuh/OWdSzvA6g2O30sdwitDTLIGv/LL7+co0ePdkzxz+fz1Ot15n3Z+n09SOIvhBBr4MXyi5w2mmtZK2ZIUr2IhTSYrTX+4OP7CssCIzYJJfHHsizCHk/6OiwmdqbJ8LDGtjWmoTk55nH1sYWl3wsG69iHYcjsbDPhWayO22Gz1d8k7vkT48UuhrbW0oVsVlPTQ1hqcBP/crnM9u3b8TyPMAyxLIt0Ot3Hib+PEWVo6OaxVkHz2H8p+ACbgxQzjbPdCHPDsFA4Nvh9MOTUdd2OYx9X5gmSLIY7ghFbZJSLHuDEv16v/8TEv9FoMO9J4r8eJPEXQog14D33NNlKc3hT1YrwK5e3Kv4mdi6LUh6+rzBMUIlFFPhdjrh7Ftf4Dw2endfZAAAgAElEQVQNUavVuh3OW9au4Cet9l6lGB5OSKfBtDRWbLCzDP8Y/FsCbUOfJD0XynXd9q5AyxN/nxQpFaB7/OLPilb/KEYBmQzUdRGL1on/ACb+8/PzbN++Hdd120lyJpPB9/vj829F4h/4qDBNnYRYR5itxN84eJDx2+9k9i/2dCnSjcFU4Fka3+x2JG/duce+UptFe8OY7jBGbJNW/kAP91tc4//KK690LIcpFAos1Baoh/UuRjc4JPEXQog18Pa/+SbWv/wDulajakUE1Z3Mpw2MxMTOZEkSjzCkXfGP4v448X0zFtf4Dw0NUVm293Gvak91T1oXAExzWas/XDozjKUVD4a78UmDP1iJv+d57cR/cRaGHYVorVAkfTHcr6PVv3Win80kVPUQKVodHgOY+JfLZbZt24bnee3W6P5u9fcxwiwNEuLEI++3PhOefYZJV1F6/rHuBLpBWEphJf1R8V+R+DdKWN4QBc/GiO2Bb/WP45hsNsull16KYSyln/l8nsarL+KdPYV2Bnv2zXqQxF8IIdZAbEA1BZRmKduKdG2CubSJmRjYuRxae5gmmLYCbRFJq3/fVPwXFhaaW3otDvRSBlddFfFv/o2LZWl+5cGrAXg5fhsRFvRJtfNCeZ5H3HpuFtviU1GEojXdvMcr/iu282sN88rkFDU9PPCt/ouJv+d5ZLPZvqv4Z7PZpTsCH8IMjtIQOeSWvbRHXVjI9H7C+1aYWpNE+f6s+LvzpL0MKT+NGaSbw/0GOPFf9I53vKPjdqFQ4LKvfgl/dgr9lf/SpagGhyT+QgixBjxlUE6bUFmglEozUU9RTptYCdjZLFq72LbGMFVzjf8AV/yXt/r3Q8V/YWGh2cq42OpvGigF6XSzwyPjNU8OZ5ItzWF2fVLtvFCe55HP54miqJ0k21GIppUE9fiJ8bnb+SVRCBoyeTXww/3m5uY6Wv3T6TRKqb4ZcHnugDft+RDlcCyFjhoUg6Wt+wwUejB38gMgJMRQUAm24L3uHmMbn+u6HRd9qt48aS+LQvHzD91CmlbiP6BT/Rff45/85Cfb903VpyirMtqtEBrAk090KbrBIYm/EEKsgeP6Mo6lNsHZs1Qsm81OzHzaIBVr0rkccexg281EkNgm6vH25rdiseJfLBb7puLfTPxbyYxa+qq1LEWMRUPnGTXmiLEGrtXfdV22bNnCwsJCez28qWKsyG7W/Hu84n9u8hclEUZiYGbTBDq9tMZfD17iX6lU2LJlC57ncWjmEMc5DtA3e9lrrTvamKPAhShDYChM5VFcdn33W/5t9MfljjfnocxDBDoCfwjX6P3jf27Fvx5USQXN2zrOklUOiTZ7/sLmW3XNNde0///Z8rO8EryCY2vSsQKzD1o/NjhJ/IUQYpXpJCFUBo6lYHqKgDSb4xrVNNgJpAsF4tghldKYlsJITMJ4cFv9F9f4Dw8PU61Wux3OW1apVJqt/u2K/9LJjG1DhMXL8dt4h/k0kbbA84mSwTkZ9DyPbdu2MT8/317jrwmxw+a+7r1+YqyU6khk4zDASCzU//Q/45oZrHe/s/mDAaz4a63JZrO4rkvVqxJbcfv+fuQGDQhzJJiYKmAoUHzV/d8BeDYa3D3Lg298jbEzz+C+cgzDGaNu9f52rucm/oHnYMbNz/5I261Wf4UOevvC5moqeSUiI8KxIBvRqoSItSSJvxBCrLY4JlKKOEmhp6bwdZpNzOKailSiyRWHCIIqtg2m1ZzqHw9Y4v/MM8/w0ksvAc3t3Wzbplgs9kXiv6Liv6wCaNrNiv/L8RVcbT5FhMWJ2gnuf+b+LkW7/jzPY+vWre3EP5vNEhshdtg6+e/xiv+5SexixZ+RUY5vuYT0L/+75g8GMPEHyGazeJ5HzauRWP39HLhBAx0UiDHReOQ9g+PJFUBzh4dBVTl0kEo6pjE3Bc44ddPudkhv2bmJf+Q7GK3EX6OwCLGiFF4kA+wWlZ54GOfJH+HYujn/Qir+a04SfyGEWGU6jgkNRZykYeo0AWkmjRkCwyAVQ35kGM+rYFka0zIgsQgHbLjfq6++yosvvti+rZSiWCxSr/f+lj4LCwuMjo4uVfyXJf6WCZG2OJHs5ErzWXRi80z1GNVGuUvRrr/lif/j9uMYhkHEUuKvw/56L0Q6wkgUWCZxYmFlWq+HAU78Xddl+MB3GXl4/4qf/+2Lf8uZxpkuRLb63MhFhVliTGLtYgc5XN1cB17XQ2j6t9vhfKanpymVSsy7ZWopjWND4myiYVjoHu/0Wb7GX8cxke+i9LLPfiKsMI0TNLoV4oaik4TG9/+exoHv4NqQDaXVfz1IT4UQQqwyp1olUgZxYjUT/2KKSeMsoQGpJMFMZ1AqaLb6G0A8eFP9XdfFOWfrHsMwSPogGVqsYuskaQ6sM5ev8YcYk1CnKGYDjDDDke98FQB95X9AjY11K+x147ouW7duZe7VV4gWnmTh0X8l0iFWaGMkBlEU0Munf+euV4/iACMxwbJIEgMrNdiJfyaTwXcciqdPUEuBDpY++6Ik4t4j93L12NVszW/tYpSrw4lcUqFFog0CPAyviE+zKuySpeAb1MIaQ6mhLke6Pp544gny+Twpbx4ryNCwdTPxz1rNHRB6uNW7o+LfaBAYCitpfhYoNKaKsII0jbDORBfj3DCqFQwgUeDYmtPu1SSWKRXpNSbPrxBCrLLZs2eJDIiSDHrqFD5pJtVZIqVI6QQsC8uKm63+tgGJTZj0dnvzG+V5HrOzs90OY80opdBJ3NyiTi1v9W+u8VdoMhN5jDBDOatJJcChH3Uv4HW0uMb/0gP7Iazw6ud+jQXDJ+tlMWKz5y+C/cRWf9MiSUzsAa/4ZzIZokYDzwLX1uA6nDXOAvCd49/h1otu7ZuZF17kkopMYkySxCcKh/B0c/CjrzNkA4ta0PsDTS9UpVLBdV0qUZ2Fxtto2JB28zRMs+e3Ne1I/MOQusoyrJsdbM1W/7hZ8R/AVv8kSVYO8Jyba/+vY0HobsG3en/I40Ynib8QQqyy8uwMsVLgDVML6oRJhk3GWYwoTSrWYFkopcnnNZalULFFFA9e4j8/P9/tMNZUnMSopLN90Wqt8QdITw6hwiye1UoUl02C72ee5zE+Pk5yZopsaHBySPNCPmH7XA4jMQiT3k78zxXFrcTfslAqwc60Xg8DmvgbhoERBvimxrUA12V/YT/feeE7PF16mps230TQo6+Bcy/6OLFLOrCIMbGiiIYu4utmcuiTbn7298lFjgtRrVbxPI+5xEMtXMp0ISHn5HD6JPFvb+cXhdSMDKPJ0kUdkwgzzOAEg5f4L27b2mGu1P5f14LI2Yzfy61ePUISfyGEWGVzM631/O4QRycScpUJhlQFM8iRThJUa833Bz7gYtiqWfEfsOF+rut2bHnWj5IkRmkFyyodptVc4w+Q2TyMCvOM1rI8G10Dqd6fbH0hFitjZ+bnmS7/NCeHNCVDs9mPMPpg2cu5la0giTFba/wtK8RKtX6uNXrAkv/F58aKYnwLrAR0o871mev511f+lTvffSd2DGHY20ngIjf2SUcGCSZGGNLQxfaFP19nMBKbMByc7Tyr1Speo86MYcDc5ZwsKAqejWNafZH4t7/Tooi6kWHUbh5bhcZSEaafwR3Ain+tVqNQKHTeOVdCa9BA1TaJnUn8pLdfA71AEn8hhFhl86U5YgUpp8DhLTFjc5NklAdhjsyyE/2bbgqxbAWxTTxAVR9Yudd5P2om/kZnxd9qtvoDZLYMQ5hl69wwDV3o+Wn2F8p1XTKZDCqTwfO2Mpey8HWaoqpiJAZBny178WONpTVYNul0jNYBGAZKQ9LjFzneLDOOSBQYGtyD/52rjz7PbZWfIvPE05j/x2cJ9tzd7RBXhaM9MpFBrE2MIKCuC+RUs/3bJwOxReANTiJYqVSI5xcopVIk81fyStFkMvQIVe9X/KHZzQJAFNFQacbSS59lFhFGmKURu12KrnvO932vZ2c5nVzEifhyPJUiCYbwo8G5CNYtkvgLIcQqq87PExmKtFPksa0Jo+UJMsqFoIB9ToXPsNRArvHXWq9c83cef/H0X6xDNGsj0Umz4r98O7/QW2r1H84yNn0p7zy+iZj+OPG9EEmSYFkWN1xzNX6SxdEFAp0mZ9YxE5Ooh7tfzreW1U80dqLBNMlmNWHooEyFmShCf/CSAAA7SajrAnVdoPKtv2TzK2e4+rd/E/2/fZRUrUH47FPdDnFVuElIJmxW/M3Ap6EL5FVzqrun06jYJhqg1m/TNNHVCq5Kk3OynCrCpqjWvBjq91HSF0U4RorhXPOzYHE7PyPM4ESD954PgoDUOR1tlfJpIm8SlyyBThFFBfxw8J6b9XbB4zOTJOHzn/88Y2NjfP7zn2dmZoYvfelL1Ot1LrvsMj796U9jWRZhGPLHf/zHvPzyyxSLRT7zmc+wadOmtXwMQgixscQxoVJkvDynipqr/SyZS4rooEBmcYu3FtM2IbF6OtlZTZqlNbJe5PHj6R/z76/9912M6I1bTPySJMbQRud2fm6VSDc7AMxsikwjQ8oeJYb+OvG9ALmijZodYXooTaE8QX6oihGP9vRFMMdxyOVyHff5CdgJrcRf4XlVTCPBig2iPmlpf6OsKKSUTJJgUHNfoegvXSyxEoiymdf4697h4pMNFZXWhb26LlJoVfxNYlRiD1TFP5PJoKsL+DrNqKs4PZRwc1RlRlvg9/Z3YMd8hygiVgbp1FLibxJjhjmc+GyXIuyeIAhWVPznKmeI6lvx02cJVAozSuHHg/l5uJ4uuOL/3e9+l+3bt7dvf/3rX+eDH/wge/fuJZ/Pc+DAAQAOHDhAPp/ny1/+Mh/84Af5xje+sfpRCyHEBqaSmFjBiGuQCwxQYL3rOnRQXJH427ZCxynCeLBa/QFSqRSe15nsPpN6hhOVEwC8Wnu1504EwjBst3vGurXG31hq9TfdGhE2Cg2tCdAOuYGq+C+eIC+4c4z4EEYF7NLbyI5WMWOTMOrdxL9Wq1EsFjvuC+JWxd+2KRQUvl/HNGgOMhzQCpcZx4TY+KSppzRDAfz97g+gHnyEVKwIjf6YfeDqkGykiLUBWrcq/s2Bb7YKIRq8in/K8/B0louDKuVczCbKRNj9deEzikgwsCxIK4+AFIbSWH4aJ+6jx3mBfN9fUfEv1acxnHECnWl2fMUx/gA+N+vtghL/ubk5Hn/8cd7//vcDzS/tZ555hve9730A3HLLLRw6dAiARx99lFtuuQWA973vfTz99NMrppwKIUQ/U1oTG7DJi9gxn4NCEYaHUWGOdNL5eWjYBkZs9XSV882amJhgbtmWPgBWvMCpE08DcLxyHEP11oq0arXKyMgIAIluTfU3llUz3So1XWwu/Uhn0CgaujBQif+ihaDCpB8yNnUFhZlLiSYy2Frj9fDAu3q9vmKIlYfGarX65/MmrlvFNBPMxCAMButEd/F80IoiIm0R6hTVtKbubmchX6Cmi3zL/TXm42yXI10dzcQ/IaF58c/ReXI0E/00PiQWoT84iT9AOgjwSXNFMAOJxaSaabX69/bnX8cSnygi0QZ2SpNRzQsdAHZo4ySDd7HvfK3+c+4cBSeHSkxcwyYXR/jS+bjmLqjV/2tf+xq33XYbrtt8sdZqNXK5HGZrYNHY2BjlchmAcrnM+Pg40Lyyl8vlqNVqDA0Ndfyb+/fvZ//+/QDcfffdTExMrM4jWieWZfVczOK1yTHtT904rvlMmshQbPF8Ln3yIl4amyBbKDL++K1k4i8zMTFBLpdjfHwcZ3gYI3EwLWOgXn+5XI6dO3cShiH5fJ45NccVepztLz5J7aU/YuL//TWmnzrB2+oW40NDqHNOGjbq+7VcLnPRRRcxMTFB2TRQWjEyNobdivWsU6WiR9lmnKY4eQ1Qw9F5dOximTC6AR/Tasvn80xMTFCLG4x5Cdtffi8aRerKt5N6uIKve/e9cPz4cbZt29YRf6ghlWjGN21mcjLBtjW2BcQm+VymZx/rG2FZFqOjoxSLxebnn2URYROQopaCr5z9bbYeHWfmvu1k4piyzjM+Pn5Bc0A2Cq01uVyufTz/07/8J+IE8spFa5vFR6JU8+KHTQBJirRt9uxr4I1+DufzeYpofJ3hUvMEueoY48YskbYopmwyPfo8AB3HPsjnSTDJZmzSeM1BjoCZWGCqDX+8V/v7NZPJtD/3F83G8+TqBVJ+mmpBUYgjAh1u+Oem171u4v/YY48xPDzMzp07eeaZZ173Hzxfdf98H9y7d+9m9+7d7dulUmnF72xkExMTPRezeG1yTPtTN46r77jECiZ0hcbULVz203XcKEJVLsLOR+14Tp48SdbzMRKThucM1OvPcRzS6TTHjh3DaTT4o+/cxe9e/B9xrIS5+WlKpRJnv/HnpEolSt5XUB/51Y6/36jv1+PHj2MYBqVSiTDwUdpgoVpDtWJV9VprnW+NWhCiaLb/WkGD2flp4g34mFab4zRf6zOBQ9G30CgUGn3xJaT/9UkaYbwhj+2FOHnyJJlMpiP+INHYOmGuUmHrVpOZmZOYKkEnJqXSWfLjvflY34iJiQmmpqYIw5BSqURUrzcTf52mltL8TPwkxtvy/MZvvIuv/7ezTBsGpekzKLt3trj0fb/9+NzI5e+e+zsuL4bciIcVpiigqANkskTaJKM8dJRmYb7Us6/3N/o57DgOqt5c7rRVncasbGNclYjZSq00R71HnweARqPRfi70XIkEA4yIjHLx9dL69tD3N/zxXu3v11Kp1P5ehGauOBvXyDkFUn6G2ZRmcxzgRt6Gf242qm3btl3Q771uD+Xzzz/Po48+yqc+9Sm+9KUv8fTTT/O1r30Nx3GI4+Za1XK5zNjYGADj4+Pt1s04jnEcZ+XejUII0afiOMZUECmY1GX2hx/gPbddDpZFjIVFcy1/Pp+nXq+DaWIkBpEevDX+mzdv5uTJk9z01BOceugf0L/3fzHjvJ1XlY0OQ1g8SXimdyZ8LywstFv946Q11d9c9lUbhdR1gby11Orv6DyFQFELal2Ken1prdFac1YnTPitJS6GYviaa0klCV4Prw48X6u/r3VzNw/L4sMf9gmCBQwTVGwSDdAe7mEYYts2AFGjTqQtIkzmUimGfU1hsoJSkFXgm0bPbW/peR6Z1tyOlysv86nrfp3jwxFpFWCFNkOtTnYzn6ahCxRUFRKbIBiM1u/FHS9SgY8GRo0ySeWy9rBDgt5u9e8QRcQYWJYmjd9u9Qegh5cyvVlBELTf+wBUK8QJ2CoiFWTwLBiLGzSSHv7w7xGvm/h/5CMf4d577+UrX/kKn/nMZ7j22mu54447uOaaa3jkkUcA+MEPfsCNN94IwLvf/W5+8IMfAPDII49wzTXX9FSrlhBCvBXz8/MMFwrEBoxtSfHS5l9gxy9eBXZzoNti4l8oFJqJv2VhxOZAJv5bt27l9OnTvOfI45wuJuinnsQJx5kz8/DSsfbvqcuv6GKUb0ylUlm2xj/B0AqWzym49joaukj2qh2QaVaBXHLkAoN62OhGyN3husxaJpt9n6oepjiimLzoItJJjNvD58XnS/wDmq3+WBbFYpFarYaVNprD/bzBOeZhGC6t8w0CImxMYsp2inGVoFtDMTOAb/R24n/sob/lus//Ef/n/i2k8LEji2LQPBdOD6Wo6mEKqo6O0wOzs8PieyOJXVJBmhE1T/Lgb7aHHdbdCrPObJejfPNWrvE3sW3IKBePZbtUDFDiPzMzg9Z65Rr/qSkcXWCzMU3az6DCLGNxnYbMhFtzb3pq0kc/+lEeeOABPv3pT1Ov17n11lsBuPXWW6nX63z605/mgQce4KMf/eiqBSuEEBvd3Nwcw4UiGoPx0YSrrzdQCrAsssppTnKmmfg3Go12xX8Qh/sBfOxjHyO0m+t8K2nwdAZPZ3H++btkYnB1BnroZGB5xT9INErTUfFXe75CqbCV8Ff/HaQzzRZ3rcj49sAk/kopqFVxjBQjRZPonTey41d+ltzwCOkkwdO9Wyw4X+IfJpqUTsA0sW2bKIow0yZGbBE16l2KdP0tP/nPtZJ8O7KpmimGc83dMKIoImNCYKieTvyP/91fcOnxeS4/O0xK+ViRTdFXxIZBJqtaiX+tuaPLgFT8q9Uqw8PDOMoh5+QZUgs49Z2kWt+Jj9ee5b8//w9djnKVtLbzs1KKzLuvIcGg8dM/2/zZACX+3/jGN2g0Giu284uefYpGPMSWnWnSXhorTFGMQxoY6GjwiiDr6YKG+y265ppruOaaa4Bmi+bv//7vr/idVCrFnXfeuTrRCSFEj5mbm2OkWCBBMZqu8clPNk/sVTZHBg9zRau/hZmYROds8zcotm/fTjI5iYqrzGU1vs7i6SwnfvSPbKul+Pvibn6zhxKASqXSHmYbJQpL647t/NSWLVRSOSiUIJNpr29PBWnq8WAk/gDUavhkGCpGbNp1FRe930fZLuk4we+d6zwr1Gq1jsRfJwmBYZDWGmUuvQ6stEWUmITeYCzvgM5W/0yrOmqHNlXbZCgfMjq6lUqlQs5U+IaCHksAlif+kQGpRBGQJkXAyPwYFynF/2eapDNQ1SMUVRWdpAmjwaj4VyoVisUiVbNBsTqMpWK2GqfbP58++Pe8+sL30dfctmKYay/omHG2ONXfVmTuuB3byKDfeT38M5Ak1IIaGs1Qaugn/nv9wPM8PM9bsZ3fqed/jF3ZytYbt2B/bwY7TJGPI2ZMC4IArDeUnoo3oLf2SRJCiA2uVCo1K/7awDY1N9zQSlp/+VdIFy1S//E/AMtb/U2M2CDSg5n4A5Av4Nd3UMppbBXikuNE9Tju3LsIdLqnKgBJkmC1TloiEgwNGJ1ftUGQQusqLKuA2EGaejwY23ppraFawddphobgF37B5/LLIzBNMjrCUwod9+b7IYqizpbWOGol/p2/Z6RtzNgicgfnYs/yin878Q/S1GyToWLC6Ogo5XKZjKEIeniNv/aW5jYEOkVK+Ww+u53LKgZRK/GvLK/4R4Mx56FarTI0NMR8yqNYHUb91m+zfbRGsvt/BGC6oIl9F06f6nKkq6D1naVsi2xOYWVtUrlc82dJwoGTB/jx9I+7GOD6cF0X3/dXtPqfOPM0QfkdXPr+neQCGzPMUIhDHMsEfzDeD90iib8QQqyicrnMcKFAgoFhL7Usq2KR7M/dhP2//DLQrPg3Go3mGv8BHe7Xls+jG5t5dSihEDS3ejoxnDBVuoVRowxh7+ztu7zqEyVgar0i8TdN1Uz8M81Wf4C0n6YRD9AJT62GT5riMFx/fUg+r1FKkdYJnmHy8MkHux3h6ggjQqWwjc7lC1bWQiXWQK3xXz7gK9N6OuzQpm4rhoabif/8/DwZGyJl9NT7HpYS/+TlF1E0VygFpEnjo1vLVxLLwrTi9hr/OM4QDsga/8VW/3LKp1AfghvezcUfuArz3TeigRljlNlwB5yZ6naob10UAgpsi0xGY1mQyrYG/OmEYwvHqAbVroa4HjzPw3VdwjBst/rrOOZ49Tj58jYyN1zNZAITL7+LfBLgGib4vfW+7zWS+AshxCqan5+nmMuhUVhmZ5lv8QQAllX8U2nARMeDm/iH2TRR7RKOjULWy6CBhg3aH24ujeihiv9ykdYY50n8bRvCcKE91R9alU8GI/FXSkG1SqDTFEc7n5uU1gSGwbeOfbtL0a2yOCY0DFLnjC2wMnZzqOcAJf7LW/0v3rIZaL7uXUtRHFKMjY1RLpdJWZpY92bFP5vNErz4HKkYvuj+Hr5Ok1JLiYy2U6iiTUWPULAddJwhigcj0alUKgwVi5A0Zx6waTMf/rDT7nwqJ+PMJpth6vTr/EsbTxzHGMs/5xe/s0yLdFpjWRq1ONU+SZh1Zgcm8V/R6v/KcY5bKS5JWaiRUUYzEZlT7yarPEKs/trdYQOSxF8IIVZRHMcYaDQGptV5tt9M/JsXA9pr/FtrQns1uX0zoijqOEnydAiVi3hu1CLj5rAim7plkVONZlrcQwnA8snOzYr//8/ee0ZJdtV3u88+sXLo7pnpnqwZ5ThIAkk2QoFB4IuJjly99pWx8YvvsmyMsXnveu2LgYXBhAUW4RoMGBZgExYGB4KQAEkgJKRRlkZh8kxPT+fqSuecOmnfDxW6q6vTjGa6q2rq+TRVp6pnnzpp//bvH4A5ud0A6XRIuVxqVPUXoprjXw67X/g3IiKKNeHfrzdtNwipKCoHRp+utnTsdHwPVxGY82ZbalSHUMNzzo7CbtAc6p+ORECC7hkoboxUHw3HXzMgRO2o6x5mHX/vwPMEQYTH/JfiYmBQFTK+VFFMFfvKSyi8+lYSr7iy6vj7Z4fwLxQKpJDIQKCpHqRSXH21B6aJAEoyge31YY0cWeuhnjTza3s0nuda1fHXdUCtrvqLICRpJM+K9q22beM4TrXNce05KJ95hsNyGzddcQKAVMLHltUaSD4aVHrC/0zSE/49evTocboJAiQCRWu+xTYmAFSFv2VZjcrunEWOf90Za7z2bUxXYyyqErFjRK04Y1qSc9QD1UD4DloUmRvqH8ia8J/X0jaTkbX6DjoMDgKgSIUw7Jz9PFUazk+xCAiUdLJpuykkFUVweOYg/pc+vzaDfBHI+R0oggBPKJg0nwOBEiJCDdc9Ox1/x7XQfB3dNdCcOJF0pOH46wYEqB113cMc4X9oHzP+enyp4UoTQ1SFTEkmicUlLhWKfTtIZVXCwDhrivsVi0WS5RI2UcyoNbtIalYXvy3ipAspjk/sX8NRnhojIyNs3Lhx9g3fr17x2qzjj6YhEQRhQFyP454FkR51tx9mF8Wf2/dz9PEL2PGyPgDS29PEVQsZgQCtl+N/hukJ/x49evQ43dQLk81zeiMRiVoL/1cUpSoSaq4vXmdNcl8Mtm03ql8D2L5F2nfJGyrZiiRqxdHzg2yP1jkSiG4AACAASURBVIo8dZjzV6ca6k/LedDfLyiVStWJ0Bt/A377LQBIvzML2p0Mtm0TjUaxitOovo5INle1NgixDDADQf74vjUa5akj5i3y4Pt4isCYN9uaLM4gAh2/cvY4/k3C37NQA42YL9AqMUQiSTQaxbZtjA51/EulErFYDL8ww7Q/yE51X6OqP0BZJkgkIQhKFAoKiURIICOEZ8mibxAEqGNjFMM0qfjk7AbTRA1UFF8nO5PmWKHzHP+FhD/QcPw1DahFBKiux/bU9lUf41ogpcRxmoX8T3K/5JwD58NFFwOQ/sv/SfyNt+Am1J7jvwr0hH+PHj16nEaEEIsK/xtvrNDSpShSc77PkskfLOD4BxUygQNOmsFKteKzMXYR23bQUaH+891eD2rt/JoftdlsNd0Bql2LfKpiSJwF50DdFZ0pTxCxo5BsdvwjQjIVd9mRE8zYU2s0ylNjfgpL7U08Bcw5xf0URWGqOF0t7lc5Ozo5QHOof8Wz0TyNtOdBJdUQRQC6Lglk5wn/qakp+vv78UOPgr+OLcoRHBnBrDn+BZkm0yeoVPIMDxdJJMDDmH1enAW4I0cpBX3EEhOzb5omqq8RL6VI57Mcq4yt3QBPkYWEv0SCpmOaYBgSsn0IJLGyy3mZ89ZusKuIaZpNwl9KSXl6lEglOiv8+xSSAwaa5uNLrVfc7wzTE/49evTocRqRUkJYm8gpzcL/2mvd+RpwtqXbWeD21ml1/B36AouwPMhQxWb9+EYGD+wice4GJCA7JAfWsizi8XjjdRAuXNwvmw0b/45EZEP4d1po86lgWRaxWIy8ncN0ojDP8Y+qMJ10OHdaIe/MrNEoT42JiQnWrVvX/KbvtxT3SyQSlDwHAg3fO3vCWpscf99BC3TWOT7pw7sgMbsApJuCkM4r7ue6bjXUP/QQoUqfMsV4ONjI8S/INJl+nXx+jEcfPYQZqy1wnAULfnVGxw8QFrYgYnMW9UwTzddIFtLErTgnwgLS8/j+oe+v3UBPksnJyeZrf47jLwRccokHfdXQ9l/bp3De40eR+zsvoulkiUQijVB/AIaPgeOjxgxYtx6AbFayfXtAJCrw0XiusL81ZarHaaMn/Hv06NHjdOMv7PgvSKO4X2dNcl8M8x3/oh+QCiqIsctYl1aJiTI2Udi2vdrqsEPaes3MzJDJZBqvfSlqjn/zefDOd84WdYpEJPFkTRWeBc5fuVwmkUgwU8kRXVD4K+SSFsMTtzDj5tdolKfG6Ogog7WaDQAjpRH2TD+BLyCizk63UqkUvioh1PHd7hf+9XBfz/NmHX+/6vj3hTaR4aubHH/DFNUc/w657ufjhR5qoJIVU4yGGxs5/gWZpn8oyo9//D1Sqa1MTNfa1p1Fi74npg8TKfYxY8wufmKa6K5JspBhnTqFFUZxTxzjHx/7x7Ub6EkShmGjeB2ArD/Ptep7v/VbNmSrwn/rsQL6X7wD7vohsssXeyORCI7jzKZAPfcsRZli41bReC8Wk7zlLRaRmMBH5wMT/4pzNrW2XWV6wr9Hjx49TiNCiJrjL0FdwS22Hurf5ROAudTDvesUQ0ncD0nc9xdkN+hklWnKMonYuh01UPHCzhAAuVyuSfgH9Rz/eT3c60Ee9X/HUwKJOCty/EulEvF4nLxbrDr+qeZQ/5gJhZjD9PivMOOX1miUp0aL8H/65xx6/G48FYw550AymWT9lk2IQD8rCrvt27ePb3zjG00tvRy/2tItLoqoBE3CXzVUJErH3hOdQKJJ6P/j32RU247xlt8CoChT9A/GsO0cur6OQ8O1InZnieMvhKBQGCXiRCnE51z3ms7Fe69g/UyKjdsE6ekN/OtTXyKuxxf/Y+2O7yMQCG1O15JEglAIqIW+SwC7u2t81IV/w8Hf/wIFmWHLBfNzHiEWV3BUyfPucUpuZ937O4me8O/Ro0eP04iUEoIQEI32PUtSL+53Fri9deoF3uoUQ4j5krSYIbNOYe/V57LxjS+Fvj6UUO2YdlfzWzr5EtQFHP+5mKYklqptD/yuD3EslUpVxz8oYjqxFsffNBXKMZvxiRvIh51V8X50dJShoaHG69JnPoZ19/cIUTD0WeF/8cUXc/GuSxFnSah/qVSiVCo1hfrbgYPq6yRUi6SSb671UG990mGh/nWcEMxAkt21ldELdhN5468DVcc/tSHC3/7tX1EsqrihVevocvbc+538NLqnY6dnF0gJQyJUWK+MsvG8GEOHL+bzR7/FS+/Zh7zrzrUb7IthTqh/HSHEbIRfHbu7a3zUhX+dsFAgL9Ns29Z6zseSOuMDU7zy8SLFr3x2NYd5VtET/j169Ohxuqk7OMs4/qqq4tfbvYVhd/QtXwF1x9/2bZ6ZfIYSkoTvM7BJJ/uHv4k9pLHjxk2g6yiBih90xu/SkuOPRJNhS47/XCIRSSIlUJWQUNKxLudKKZfLVcc/sIg6kdZQ/9BG8wzyM5cwIx0eGX2E0fLoGo325JienqavlscLUC7nsDUIUartvGqcc845rN+2CRkaeB0azn4ylEolyuVyI9Tf8R1Kfkg0CEnccBWprAo7zp39Ql0sdej90A4keiDp64exMQUjXt2fgkyTHIzwyle+HNsWKJHafnb5NV9HhCFlq4Duq7hzIqO44ELEuVuwrtzIxosSlIvn8r9+VEHPF5HvvH3tBrxCwjBsfXMB4Q+gxOdFMVjdLfxN02zK8bfsGSpuP4NDrQvcRiJOopjm5cdUit/4l9Uc5llFT/j36NGjx2lE1EQ8sKzjn81myc3MzE4OuryNzY9//GNg1vEf+eyHuPejf0xJUYlLyTV/cD7mtVczNHSEX/91BzQNNVTwOqTfcV3U1vGlQAnFkgtApimJxSS6Jgml2vXnQKlUIhGPk5M+KTdsrepfnsEoDrBDHMURGvd++A/Z/+G/XKPRnhxSykbeqvQ8jpNkv7K5Kvz15s+qcbOa438WhPqXy2XK5TKu66LrOv/7/v/NqBISD0KSf/pWUv/jDYhYDKDaDk8o1TDoDhL+vu83crwrMsSQkr4BmJpSUKPVsGZPGph9CTStmtfs13PCu9zx92rHUfM8xtUUQ0oBs3a8AYSiEP/dN3H43CTpC4fIh1leu7/2TJybF9WmTE1NMTAw0PzmIsJf1lL7pAQtAK9UWI0hrglSSlRVbVoYKdp5dCeGmoy1fN5IJLn5R68nVRGUWjMBepwmesK/R48ePU4jUsrZh/4STi9AX18fuVwOWVcFTneH/X7yk58EZh3/0n0/Ipc7TllTSCB429uqod1C1H46XUcJVfywMwSAbdvE5kxo/brjL1rPgzAMkVKyYUPI0FCAoQfV3uVdLvzL5TJxIahIg5RZQejNitgoTkJhM+epz1HB5Ag5xp9+YI1G+yKwbUb1JBNqkhAFVWuu86AmYkjfwAvcsyK9Y26of8Er8NNNJeK+T9+gynXXzS7sJRIJGld7Bznhc6M9nBD0MCSaUonFJOgGQtSOcS3CJZUKkbqBRHR9jv/73vc+pJRogc+ommarNt1U4wXgDW/wSaWGETvOabwnJIQ7dq72cE+a+bU9gDnCf96KXy3F7ef+jUw651IsT67CCNcGz/PQ5i18FCt5zIoJ8UTL581kEkUqPGddS0lv2dzjNNET/j169Ohxumk4/ktX9e/r62N6enqO49+9wj8MQ/bv38/09HRD+I97kheM9ViqSkIVrV/SqqH+bofk+M8P9fcRKMgFz4MdO3Zw4MABLrvM49JL/WrvctSuPgeg9huFARUipGKtx1VxLPz8ds5Tn8PFRK3EOBHVkB0QEt+oXA1gWeR1FU+ohFJB15rFvWqqBBgEhB3lbJ8KdbffdV0Mw+A81vPMOptk4BFNGVx7bbPwd+v3zw76XSYmJhqub0UKzDAETWNwMGxUdgcaOd6plESr3ys6aIHjZJFS8uijj1KpVIgrCkVNZ0DzWoR/NitRlBC2bG0UQ9VD8AbXLfRn24r53VwA8H0kEvRm4Stq+3083IrqJMmXulf415/zcyOhim4R0zVgfsoDoM5MA/DT0m8wnUi2bO9xeugJ/x49evQ4jQgxx8FZofAX9VDwLnb8Z2ZmuO6663jqqafI5/PEolFGfJ3jRoKyppBcwBVH19FDqCyUQ9mGlMvlpqKFAdTa+bXu20tf+lIefvjhxmuzIfy72/GXUiKKRSrSJJVYOMTZf/ytnKc+j4POdPk8DhtZKBQX/GzbYpUoaSr4ZtXx15sXtnRd4Km1MOZyd1ewrrdwDMMQ5bFHUb7+NS46niQhQ8Q8RzCRSFAJJQI6qp3f1NRUo4+7E0qMMATdYHAwQKQzcNHFsOvKhgBKp0PUuvjp4lD/XC7HyMgIpVKJtGngCo1kVOElL3nJgp8XuoFIVaMijEB0xKJvqVQiOS9lqdGed/4coPZ8GA03ojlxilZuFUa4Nszv3gNQ9MuYlUhTF48GdnX+c8S+gqlQdH0k1FqxbMlp13V5z3veg+/7BEHAtddey2//9m8zPj7OJz7xCUqlEueccw633347mqbheR6f+tSnOHjwIMlkkne84x2sX79+NfalR48ePdaUIAhQFKVW1Z9lhX82m606/nqtIFgXC//JyUluuukmnnrqKQqFAlFNY0rTCIMIrlIhsVAqp6ZhhBI76IwJQKVSaZroBDJEWUT4b9myhaNHjzZe67okkN3r+D/88MOzk/2a8E8mF17QGTqxhf74BCeSkvShTbj9OSjkob9/FUd8crRMUi0LD4NA6oQo6Ma8UH9V4mkRPAXe/8iH+H93f3gVR7u61K8Lx3Hwv/stFAm/8cudmEHr/bEq/KtCWHoeC8QBtSUTExPs2rULKSUu1ar+aBpDQ9V9UW5+JYEngOoCVjodoieT1ar+Xez4j4yMMDg4yPT0NEndwEMjHhdc/NKXLvodJZvCH1VxvQiu3/73w2KxuIDwXzjUX0aqqWBj4RCpSoKC3b3C37ZtIpEIQsyK+KJfRq9EINbq+Is/+VNGv/8cMVswbejVjgcLfK7Hi2NZx1/Xdd7znvfwkY98hA9/+MM8/vjjvPDCC3z1q1/lta99LXfccQfxeJyf/OQnAPzkJz8hHo/zyU9+kte+9rV87WtfO+M70aNHjx7tQKVSwTRNqE1cVyz8VQ0h6VrRB1Xhv23bNu6//35e/vKXQ7nMjK4hKkl8NExzVjipqlotCKXr6GGI7XeG8IfZcG8pJb5Q0KVELCD8hRBNoeGGWXf829/hOhV+/OMfk8vVJrnFQjXUP916XEUyyRblCElRAD+CPnEenjSg0N5FsFrcLcvClQY+OhIFRWs+B3QdKlqcH+70GSkdX+XRri5zQ31zfVEyjqAv10/Czrd8NplMUgk6L9R/cnKy6vgHARVFwSREKAq7d1fv6brerO9TKYlWdz297hb+V1xxBYcPHyapa/joLR3t6kQiEWzbZsPl6xkPB/mR/WbcDih+Ob+NK0DoewgpWor7xTIaZVkVs4qTZMaZ5v6R+1dtrKvJ3FD/OkVpVx3/BXL8xfZzeCD1K7zU2E9B06DU3ZFQa8Wywl8I0XiYBUFAEAQIIXjmmWe49tprAbjxxhsbIYt79uzhxhtvBODaa6/l6aef7oVr9OjR46ygMfn3a8J/if7tUG1143keaCpS0NWOfz0H9k1vehM33HADlEvMGCqyksJHIxKZfU5Eo9Fq719Nwwwllc6I9G8mCAiFQF3Cs9y4cSOHDx8GQDeoCn+3/Se6p4JlWUxMTFRfFAu40iSZbZ2CZP/zB8QGCiRf86vEC1nk5IW4GFXHv40plUrNk3/LwkMnqE2z5oe0DwyETIoh/nSPzk596KyZJ03OHOdEYRe2jBIRdsv2eDyOUw997yAnvOH6+j4VRcGoXfe33FK9njVN4rqz94JUKsSst7L0va49/iMjI+zatYuDBw8SV1U8qRFNLHxPHBoa4sSJEwz9+pUcftcXOeKdTyVo//vhQsLfC1zUUG0R/jvPDTkYnEsEC5w0/1/lHv7r4H+t5nBXDcdxmlLfpJQUQqda3G+hUH8gDFWuyT5NBQPK5dUa6lnFsqH+UC3K9O53v5vR0VFe/epXs2HDBmKxWKN1SaNAFdXKpv21cDxVVYnFYhSLRVKp5l69d999N3fffTcAH/rQh1pbYbQ5mqZ13Jh7LE3vmHYnq3lcHcehv7+faK4qcGKpJIll/u9YLEbFjBAAKcPA7NJz0HEcLrjgAn71V38VAG98jLKqgh8lUDQSSaNxnNavX080GqU/mcQIJLak5Ri24/Uai8UaY5Kuiy8Eqmgde523ve1tfPSjH+U973kP8bhGgNq150AYhnieRywWIx6GuNJk/cZ463EdHOScN/2UDes2cs1Hb+A5X6eETlJKIm38u0xPT7Np06bG/jiqiid1VKqrVmY8Tnre+BUzwm88p/NlPUYkFSFpdmdBq1gshhCCWCzGzNgUD828CeFrvNH4ZsvxD4KAJ2sRMlFVJdnGx3wusViMdevWERYLuIpKZN51n80qlEqCgYFqn7LXvU6g6xsJlUkUYCCZbBR+6ySWuw9blsWNN97IF77wBdZdfCE+OulMhP4FvnPRRRdRLpe59NI0X7zzPOLBzwjw2+4+Px/DMNi4cWPTe8dVgQhUUv39Tffzq24R3Pepi4kIB9Xq40/ENQz3b2u7fTwdz1fTNNmwYUOj4O1AMsmMppIJJevm/V51MpkTXGBM8ANMMrqG3ma/SzewIuGvKAof+chHKJfLfPSjH+X48cXD0hZatWyqdFtj9+7d7N69u/F6crKzKlsODAx03Jh7LE3vmHYnq3lcR0ZG8H0fq1aIzHYqOMv83zMzM9TTfwsT44guPQeHh4cJw7BxLOTxYVwMYh7YCdACt7EtCAKOHz+O2teHGQY4UrYcw3a8Xi3Lmt0/xyEQAo3Wsc9FSslzzz2HUAICqTEzMYbaZvt1Osjn8xw8eBDLsiicOI4nDZTowsc1Gh1GiayjJFPEhMWoNMkfP0apjX+Xo0ePIuecp3JsFBBQ7UhPJfBb9rXexjN578PsveBBdm5buOBZp2NZFtFoFNu2OVE8wU6nwA/c2/jdN062/Cau6zJTc/rsYpFKGx/zudSvfZmbpqIITNE8r3XdGLquMDlZDV+++mp4+GGXUFVRgMnjw9UigB3Gcvdhy7IwDINnn32WcPtWJAqBtvCcX9d19u3bx/btl/Odu7PsHDiK7dltd5+fj223jrFsl1HCOIWy1fRMz2yHF970dxQe+CH9Rz1eO7WRj895brQLp+P5OjY2RiwWo1wuI4Rg8sgRXHQSEW/Rv/26192L/hObCgYzw8OIzVtf1BjOJuYvPi3GSVX1j8fjXHzxxezbtw/Lsghq4Vhz+5f29/czNTUFVCdvlmW1hMD06NGjRzfSCPVv5Pgvf4u9+uqrKVq1kFen/cMaTxUpZbXwYZ1yGU8aJB2NUsTDjM1uq4uEanG/gErYgWGwYYAvBNoCC99zednLXsbevXvRIwpKoOM61ioNcHXJZDKNyZ5TzKF5BkomtejnNTxCqRITJVQ7Rb44vlpDPSVaIhvnh6mqrT5LdtcQJ5QhBh57gcnv/9sZHmF7MOXl6SurXPKq9cT/+h0t2yORCJUgrC6XdFCOfwPfx1UUzHmXvWFIUqnmnKVoNNpoXVevaN6NrFu3jkOHDhGt/yaRhSq5QiqVolAokExK0qmAbFjGDTrwHAD80EMNleZWjlRrPRwvZBncWHum/eJnyLt+iKxFTXcTc3P8S0qJf3vh33ClQTyyeBeLK6/cDkoRV5pd3+1krVh2VlooFCjXHmCu6/LUU0+xadMmLrnkEh588EEA7rnnHq6++moArrrqKu655x4AHnzwQS655JIFHf8ePXr06DYaxf3qOaoLTPbnc8stt1C07WpxP6c157VrKZfw0Ek6OqVIBTMy+5xoCH9dx5QSR3bgMySUBEKgsvSiRSwWw7IszKiC4uu4doe1rVsh9Uk9gF2eQfc1SC4u/OtCyMAjUkozVhpdjWGeMi15vpbVXN1Ba70XXPqbF/LvO3+HdZZgvNje+/diqM8BVc9jRjpEfZO//huH/v7W4h1CCIL6gqnfGaIvDMPZea7v4yoQUea3b4RksvleEIlECOuLoV1879d1Hdd1aWR7R6ILfm7uPeIv3j6OHijYQefUeZiLF3goobLgde84gk1DtXPh4AHYv4/wUx9f5RGeeerCPwgCznvuAe7/9kfwMIjFFi/ac/755+P6MzXh38vxPxMsOyvN5XJ8+tOfJgxDpJRcd911XHXVVWzevJlPfOITfP3rX+ecc87h5ptvBuDmm2/mU5/6FLfffjuJRIJ3vKN1RbdHjx49upGG4x+s3PGHasivFHR9D/cmymVAELWjeLqHqs26QA3hr6qYQUBFCGQYLlgdv20JAgLBksX9gEYo5MaoisgZuJXunOzMNQAcawbVT0Bi8Zx2+cbfoHLHAyTVEnErwaR9bDWGecrMd/ylPS9yY4EOH1dcIfhWaQe/awl+WZk600NcM6SU1fvi8WFyxDk3VWHHjsUn/w0x3CGOf71wKVAV/qpCRJ0v/GVT5xKo3ue6WfjPTf0dGhpCqz8XF6llUG/5CPCa19jc95kAqxMLuwJ+6NaEv96ybedOn42RkMO11zEPrJkJuq3CR30+5Lou/SdeILdOokuDeHzxg9rX18dhJUCi9Kr6nyGWFf7btm3jwx9u7S+7YcMGPvjBD7a8bxgG73znO0/P6Hr06NGjg3Acp1rZOaw92Fbg+APohsSXKkUnT1iZIWN2Xq7nSVMuI5FE7Siar0PMaGyKx+OMjo4ihCAqoKQo1QrfhrHEH2wzZFjN8V8mWKHu+BsxFeEbuHb3TnaCIEDXdZxKGc3LQnzhHs2maeJmMkz/2m1sizzGibtOMFlp71DYhRz/JhYQAOk0FIIsWRtyfnt3LXixxONx/OlpSjLJhv6lFzgDRUVICD335PJR14iRkZHZ/FrPw1NEi+NvGNUWfnOJRqMEDeHffYu+ruti1O7ZO3fubHStEebCwr8pOtgwiYQh5Q7M8gLwAx8laK3qD3DrrRbaY4L7a4vCGUeQSyhdJ/xt2yYSieB7HsNmlNh0gry56G2/QUXXkcheqP8ZohPuqT3OIu67775GqFePHp1GpVKptfOrhSeu0KHuS5awZJz7vOf55YlfnsERtg+y9lCPORFU32hygTZu3MjIyAgAJoKKooDXYf3tg5UJ/3g8XhP+GgQGTpc6/gDlcplYLIbtWdVQ/0Wcv/pvkssp9K9X0D0du9Lek8B6Ozcv9HjXfe/CteY9x7RFWntGAhwZJ6x0b443QCKRQJ/JUSLOhsHFc3yh6viroYrXAT3cAY4fPz4r/H0fVxFE5zn+115b4Yormu9h0WgUX3Sv42/bdqOd26te9arZfYwuHOrfhGEQDQLK4cJFw9sdL/QXbOcHsHVrQHJgdnF/vHQJuVj3ybG6459UFQ5HE8T3X89UPCC+RIYXgKtXF0llL9T/jNB9Z1qPjuahhx7iyJEjaz2MHj1OidnifjXHf4GH/kIMZBzKJDg4/QK54efP4AjXBt/3G+1fG5TLCATrHB/pRcGYDfWfWyTWVMFVlI4J+21Qc/zVZWrcNHL84zoiMLs21B+qQiCRSOD4djXKY5Fc33r6g6JA/5CG6utU3Pb+XcIwRNM0Pv34p9mU2MRz4Ri6a6D5Or7qL3ov2L79ee71djfc0G7D8zxUVSWRSOC6U8jyegY3L31NBIqCEqj4fmcs9o2MjLBp06bqC9/HFwJj3u0unZYtetc0TYJ6KlAXHn/btonFYgC8+c1vnk1lW6JtYd31F6pKTIZYijq7kN4h/NOT/4QTSrSQRa/7aH8/olb/5cnibnJqZ5zrJ0N9PpQFCppB9OiVGE6ceGqRRdA68QQC0Qv1P0P0hH+PtmJycnLJdpE9erQzszn+J+f4b+j3KMsEU2MHyX3u48hgaUes06hUKg3np0G5DEjS0kIvbpjthEB18ld3eaICXEW0/eQvDMPmrgVBQCgErQHezaiqShiG6HGN0Ddx3e5z/uokEoma8HfQPB2iizv+5XKZZFLSt8lE8zUcr/1/F5mfwdvzAK8Md/KEMloV/p6Or3uLpv30bTzBE/5LulL4QTXKI5FIEI/HOZ6aov/QLga2xpb8TqioKKGK1yEV3QuFAul0uvrC9wlRMPTlC5IqikJYTwnocscf5tS9WGTBD5rd/Rhgq1pbR3stFI3wxPjjVAKJEcpFhb+aTNa+D3Z5Czmv+1J96qld6TDEkVGKlS3ccO/Nywp/JZlECRW8ci/690zQE/492gpVVXvCv0fH4jhOrap/Pcd/mZXtGuvXB1hhgpgnKBsSit31wGv8LnMIrCJIQUoU2HrPH4C78OTOVDrD8Z8/yUVKfAHqChsSGAkdAhPP7b52fkEQoCgKAwMDxONx7KCyIsc/mQzp2xxB83UcvwOE0X//Jzz0S3a87S95wtqP4Znono6vu4hF7gWeoWMoAcL3kV1Y3LMu/BOJBF6sTHZqPcplly75nUBVUAMVL3CZsCZWaaQvjtmq/h4BKvpyK341QkUBCdLqgPP7JJl/T/QcGzVQF23nN5+YIrFUddFnQzvQWOyvIR97hKO//AHO5BR6GC4e9RetLn6VSeDZG8gF3edu1xdFkmFABRMNn9DpJ5ZdOhJSTaXRXZOS032LIe1AT/j3aCsymQy5XG6th9GjxynR4vivUPgPDWpUgiR+/Y5c7K6WbvMnRwBlK4/hmiREgbJMLzq5iyqCiqq0veNfz19vUHP8V9jYASNuIP0IlQ5wtk+Weshvf38/iUSCcuBhBmJR4V93/K++2iW9KY4qq2HfbR8JU7tuY75gMioxaqH+nuaBvshkVwiIRLhiTOFLj322I/OZl6JUKhGLxUgKSLkuQlFh15VLficUCkqgMC0sPv5Yh7U5831CVHR9n058PgAAIABJREFUZcdRqLLqbjrdJ/zmC3/bKy254DefuCJwlPYW/qVSqbmo52OPkjMCpiMKxhKh/tSeFUWZJLDWMxN23/Gvk/B9HBkhLXK40sSMLj0v0jMZzIpJ2ekuA6Rd6An/HmuGlBJ33g1dLJMP26NHO9Mo7ld3/JWVCf/EQAZClX67dv53WYHLhRz/cqWIUTFJiiIBrZO7eDxeFQ2awBW0dbgngGVZzcI/DAkEaMu086tjpAxkEOnKUP9yuUw0GuWSXZewdftWCiEkfW/Z4n6vf72Dqimz9R/aPBJGui4/9W6hIg0CoRD3qAodwaKh/kIIMCO88rCGUfF5IffC6g76DFMXRvF9z2ME4K8bQsSWCfVXVZRQ48j4Cxx+4qfINo/2acLzCKWyUBOHBVHUADVQ8Z3ui/SZL/wdz6qm+CyR4z+XmApOmzv+hUKhuY1nqYSvwHiMmuO/yIlQex4WZZpKmCBo8+fbiyHhubjSJC5qdVqWuY/rmSyJQpp/WneA+0fuX4URnl30hH+PNePAgQN8/etfb3qvJ/x7dDK+76Np2my++mKVvOcRy2ZRQpVzZurCv7tC3BoLInMoekUM1yQpCpjCaZncbdmyhWPHjmGqCp4qwGt/xz8+t09RWC3upysru6ep8Wi1nZ/XfbnelmURj8c5rB/muBymAKSWEP71UP86wtCryyfzW+S1EVJK8FwcGeE77u+weTpKyg3RPR2xSHVvoNr+09QIpMJVchPP57qruGc91D949lEsZ4gLL19+2mkkEughHE4LwhPD8HB7dzppmrfUcvz1FeT4Awg1RIRaVxb1bHH83brwX9zxN00Tp1bvIqEKbFW0tfCf7/jLUgHdiTMZkxhy8VB/IQQSQTFMVYv8ddLi1kkSdR1AoAkfiagWNlgCs7+fbUfO5b2PDvDgiQdXZ5BnET3h32PNKJfLjI2NNV67rlsVTT16dDBCCKiHJK/Q8TdSKdRAZWg6hisNKBaxvPYVOSfLQo5/ruIQ81QSb3glEd1H/M//u2l7XfhHNaotr/z2nhi1OP5BQChYtp1fg0gELdBwg+4U/rFYjLJXplCaoqTqJAWIRYpf1kP96whNJYT2L4DmumTENPuCC9k+nqK/4hPzJTLUF037yWQyRKMuBZlm+5//DQe+/slVHvSZpb4g5hzdxzH7Um543fL53WYigRlIjqRgc0HBP350FUZ6mqjn+Bsr+7jQQpRAwzsLHH/bt9F9fckc/1Qq1WjpHNNkrb5L+wr/ehvPOpVyHre4vZrqEyyR41//vkySFAVEFwr/+oKYqnhEKhGyW+Pk+s5D/P4fLPm9SH8/pnDwDp8g+OndyHqXpB6nhZ7w77FmlEqlJuE/NTXFwMAAmqa1pAD06NFJyMAHyYpz/IXvc8mTV3P36J9zNNyGzM/wdw/+3Rkd42qykOM/HgSk3ZDUn/xfmK+6EXHOjqbtdeFvGBCgtL3j3yL8pay181vhH4hEUXwdt0NamJ0MlmURi0Yp/Os/U/jyZyipKksVdq6H+teJmh4eBthtvihSe25dmj3Ehqd3sz2vEfdDZGAsGvKbyWSIxSrkZQYjFPiH9q3miM84dUe07BYJKn1kNy0d5g9wzvnnY8iQ4ST0jexkeKy9f5Omugyej0RBnd/PbxE03SMMDLxK9wl/x3GahH/Jd9F9dUnHP51ON4R/xJQEUusox79o52BmO9OxsFrVf7HaHvXPyzQpUehqx59oQLScYOCmy5jc9X8g1q1f+uObNqMmJWWZhOeeJdzXXVFQa01P+PdYM8rlMtPT043Xk5OTDAwMMDQ0xOjo6BqO7OwiCIKuKyi11gSBjyKVFQt/zr8QNdDZH1yEI6PkimMczB88s4NcRRZy/A8YHpvzGrGBKIlE6/mXzWbJ5XJoel34t/fEaCHHPxCsONSfaBQ1UKkE3VfZ3bIsUkhKx/ZTPPA0jqKRXKL4WTQabRL+cdPHk3rbOv6NVo6uCwhuuOwEP3DfQEyUSHh+zfFfeLqVyWQwog55mWm81/ZFDE+CuuOfd4tEKjrMcUcX44qrrsIIJHnN4IXx13Mkd2AVRnpqhGHYEuovkYhlBF+daKSMGyS7spuHZVlNwr/gh8S9YFnhn89XU91MU+LT3sJ/vuNfdAp4ufOZigWYMly0tgeAJjxyso+EKLR1VMOpUp9XTlqTRK04/Rs1CoXlZWcineaZay+neO5VbMsLjrzwwJke6llFT/i3MUEXPfwXolwuN7mAk5OT9Pf3MzQ0xMjIyBqO7OziRz/6Ed/5znfWehhdQf1B54c+IlRgkVDm+Yh0mheu28Ktv52jEsbYbx3F6aKQ7/mOv/RcRk3JkCMR0QgXX9wq6uuTacMQhFJr+1D/+VX9P3Xka9VQ/xWcAlJKiERRAw036L4JoGVZxKVkVE0xpsfw0IlFFn++qapKGIbcd999eJ5HPOpXHf82bXdXr1xfn7z3v+ISpmU/CUokg4AwNBfNa81kMmimRV5meNLfRRCaeDOTqzn8M0qpVCIejzPlOSQ9IJ5Y9jvoOmYQUlZM7OlLOWIPA5Cv5NtukbqltofvA2JZp7dONFrC8ZP4le6539epd/OoUwgkCT+E6OLF/VKp1Kzwj0j8BQq/thPzi/sV3HxN+IeYYbhoOhPAE5dfyMRr30ZSFKoLRl0657/fPMHA+CDrthhEo8tfv7FYjHT2CD9IvJVLJ1SeOtreNT46jZ7wb2Pe/e53r/UQzij1CUGduuOfzWYbN/4eZ57Dhw/z+OOPr/UwuoowDFBCZdn8vrlceMWjXHf5DKqd4clDv2DTwSnknIiYTqalnd+xY7jSINFnIoTgttsWd7t0QxJ2gONfKpWanJ9nSwerVf1XGuofjaAGKm7YvpPcU6VcLhNHMulvYkTtrwr/6NJ5m0IIvvKVr7Bnzx5i0aBa+8JuT8c/n8+TzWZrAkXC5i1c95ZNxD/7jyR9nzAwFm1HmU6nMeQU+TDLT71bSE2v4/DI06u7A2eQ+qLfhCfpq/iQWKHwlwGqlUUtrme8Ur0PfuChD1Bw26uzQ6vwr92nVnjvj0QsnCCF24WO//xIr0IoSQQBmEsL/3qov2EKArS2dsPnC/+SV0Yp91M2JOYyQj5MaEyaW0kYFdQAPKu9zu3TwUOjD7F10iNhJRjYFiORWD5fX1EU+vtPsOMSneOjr+LAdHun+nQaPeG/RhQKBYaHhxfd7vs+d955Z1e7/uVymUwm08jnr+f4J5PJxo2/x5mnVCoxMDBAsct6x68FdZfalwFCihU7/vXvinQa047xlBxh23MnCD7zj2dqqKtKS47/oQO4mKS2pBb/Ug3NUKvt/tpc+E9PT9PX1weAu+cBRvc+QCgE2grOASFEw/H3Qq/tXM0Xi2VZxMIQT5pUpIkn9WWdHykl27Zt48EHHyQek3jSAKc9XdF8Pk86ncZ3neqCn2Hwtv8nyvm/2k/K91CkWFL4+6ZNXmYYCbfQl+vj4Pizq7wHZ5gwZEpK+n230b98SXQDM5CIwkaGlFE8u0gYhvxi5BdYfnsJ5JY+7vXjvMJ+fmbMwgky+J7Tdde9lLKaAgPIMKQoBCnPb7SyW4imUP8IbZ/jH4Yh6pyUvrxvkXar6WmGXFrkxuMKxWJAxAiIVwxmZronxbVSqaDrOj87di9vfKz67E5vTZFKrfwcv+mNEfb6VxLmuicCqh3oCf814Fvf+hb//M//zL/8y78s+pkDBw6wa9cujh07dsr/j5SyrR8klmWxfft2JiYmgNkIgGQySalUWuPRnV3s3r2bH//4x2s9jI6nfr0FoV8VAEvk9y343VSSiBNlPB6yoSTITx8/U0NdVWzbbnZ+Du6l4qxj04WL53rWaeTKLiKc2oW5k9z8d75GSbi1HP/lv6tpGl4QoEmdiiLbNqT9VLEsi4jvU8GggomPvqz+GxkZYceOHTiOQzwe4tG+Of65XI5MJkPFd1ADHXSDdFqiaZD0PQxPW/T8jUQiHNo5QP76NzBq7kS1MkwXukcAAFAuM2Xo9C/RyaEJTSMiA/zCdjYpw/TlBb/Ydyebk5vbrtvJwqH+csWOvxFzsYMkzx9/lE//w2uRbexuvygch6KmklDEkm2bU6kUMzMzAJiRmuPvtveibx0pJZNByKBbRqvEMMOljbtkUqVcDomYAXHbJJc/sUojPfMUi0UyySTyv/8Dy48Rz6ioUZM/+ZOVz+3N87biiQiyUEC2cSvXTqMn/FeZH/7wh8Tjcf7yL/+SdDpNqVTi7rvvbhHozzzzDK9//evZv3//Kf9fe/bsaWsxJ6VsFPIrFouUSiWEECQSiZ7jv8pceOGF7NvXC6c6XQShj5DKogW9FiWZImLHCAX02YKp1Mpco3ZnvuO/b+QJzMlzWH/JuiW/l8lkcJHQYX2OC9Y0jioBgbKC4n719nVCjRAqgN1dkxzbtjF9H7fu+GMQiS/9nUOHDrFr1y42btyIEBYuZts7/m5QQQ1UMGZ7ucWEwyX3v27JcGXVCHEveRlGNoZi95MrT6zGsFePcom8rjGw0hZ3ikLGUomOXsgm5Si/sncrf/Pw+3jNttdg++21+LO4478y4e/rCoqv85/nBeQO74X77jn9g2wHHIeyppJept6taZo4tetcmLUTpo0d/yZcl0lVZbM3g2anlhX+iYSGZYVEIhCzI+SK46s00DNPoVBgSyGPGB4mn9hK5v98LQBbtqw8ilnoBmSy1RcHevPT00VP+K8yTzzxBL/2a78GwI033sgXv/hFPve5z/HMM880fe7gwYPs3r37RQn/6enplur44+PjSCmZmJjghRdeOOW/fbrYsGEDY2NjfOITn+DP/uzPgOqN3+ugSX678+1vf5twkT6oruuiaRqKorR1dEinEcjgpB1/VVXxYzEiTpQtBYVc6XwmjQ6Z8CzD3FzPzz75Wb6oPELf5AbEjh1Lfm9wcBDbqxbLutd6qmMK3804M3iVPkIEirayYkaWZYGuV2vAtanAPVWCIECxLUJUXEx8qRGLL70g0t/fz/nnn8+2bdtAlHDR2zbHf2Zmpub4V1B9rUn4R7DRCZeNWJESEnFJxc1g21228F0qUcEkvUD3jsUYLGokDr+UQWWEsr2Vv0q9gXMiGyl75TM40JOnxfH3qp0dVir8RSSKEiqYAUR8wPO547E7zshY1xTHpqALsuIkZIfeYcK/WGTa0NnuTSKcDJFlhH8qpVMuSyJRScSOddWCX7FYJF1b9M6fczWZizee2h9K1ermjHfPosha0xP+a0A9zOmyyy7jkUce4fOf/zx33nln02fCMCSbzS6Zd/1f//Vf2EtMhGZmZhph9HU+85nPcNddd/HVr361EQ3w8MMPn+quvGgGBwf55je/ycte9rJGfmyP08svfvGLlvOgzrFjx9i6dStQLaiy2AJBj+XxPA+tNtkLAh8RipNy/NPpNCWhELXiXDaq8pOZ/8F0JXemhruq+L6PrlejF4pukXf8XJLKZ2DHziW/Nzg4iFWb9H3ngc+x91vtOSGev2iWr8xQsQeRK3T868I/blZq/erbU+C+KMplVAJ8VAI0jMTS0SzveMc70DSNTCYDioUvDWSbLojUhb/ju+iBCsbsvkWEg4a/bDX7XE5h66CFJVPdd/zLJVxpklxBYa86hvCICIvsFoUT4SZ+7b4TRN/5Tspf/PQZHOjJM79I8cnm+GuJBBE7xm88E2E0HIJCgf8+9N9nYKRrjOPgCY3Y4nX9GmzcuJHjx4/PLqB1SvpDuUQFgy3iOKE1gBkuvdiXyRgI4RGJQMSOk7O6J5e9UCiQFIIJOcBPcr9KOn1qc0vdVAikClZ7Lfh1MsvOSicnJ3nve9/LX/zFX/DOd76T73//+0D1Zvf+97+fP/uzP+P9739/IydbSskXv/hFbr/9dt71rndx8GD39KJ+sYyNjbF+/frGayEEX/7yl0mlUvi+3yhyVyqVGgJiqVyo+++/nwMHDlAul3n++edbtufz+ZaQ+UQiwb333gvQ6JP8t3/7t43ttm0vuZhwuslmsxiGwS233LJq/+fZxtTUVKOQ5A9/+EO+/vWvN7YdOXKk6qgB27dv59ChQ2syxm4gl8tVK3sDfhigSBWUZeIa59Df38+E42C6EW56cgdWeTtT7syy37NtuxEa2c407mXlEueOVBCRGCK79GLf0NAQpUoFARghPPqLb5z5gZ4C8ys7z/hlZHmQQAF1BadAXfhnIhaOjHSf8ANkbY5Qf6KJ6NL1HS699FKgmu4RCqvq+Ldpy7N614qiH2IGssnxj773b9C2b4bffsuSf2N4WOX8cyyKMtm2tQxOmWIRF5NkZqUtLkC//CLWR3PM3HRRVRDf+QNiBRv7oZ+fwYGePOVyuSnUX3o+AhD6yoS/kU4zMDnI1gOXcDA4D3vqBMMzRyhby9/7OwrbxkcjuoLajldddRWPPPIIGAYS2TmOf6lIBZONyjC+vX5Zxz+dNtB1m0hMYNgJck53dPGBquMfA/YFF3Ld1gO85CWndgy39BcokIZyT/ifLpYV/qqq8nu/93t8/OMf5wMf+AB33nknw8PDfPe73+Wyyy7jjjvu4LLLLuO73/0uAI899hijo6Pccccd/PEf/zGf//znz/hOdAoPPvgg11xzzYLbbr75Zn76058C8PnPf55bb70VqC6kPPPMM9xzzz0tofmFQoEDBw7w6KOP8r3vfa/lbzZ6C89BCMHv//7vc+uttyKlJJfLYVkWIyMjANx1113cf//9L3pfl+J73/teI5RfURQ+97nPLbnA0ePFYRgGw8PDPPHEE4yNjXHkyJHGtgMHDrB9+3agGoHy9NOzbaTuu+++RSMFerQyNTVFf38/AF4YooasTPXV2LBhA6O5GUzh8HxwMaqVZTpYvtPCAw88wEMPPXSqw159HnqQmTBDetPyM8D169dTchwkoJeyTDiTSNflriN3ccdD7eP+nzhxgsHBQaB6zx4LAkR+M47hrmjtpy7807EKDpGuEn7f//73q2ke5Zo5UN8QWYH1R1X4O6FNIFVkG9c+EEJghVSFvz5H+L/y5eg3XI9YYn+llAgB5+yUBFJr28iGU6ZcoiJNEumVR0AZ/+uv6f/9V/Fsn0l58DwAop7AjrdX3ZP5wv9kc/z7N20G4PngYiivZ89Pv8RL99uMfa29IhteNMUCvtSJJpe/IV5wwQXV+a5hAKJzhH+xKvz7lClij9xKRC7t+GezETStTCSuIL04tlvmeOl4o4BlJ6dfFgoFYlTr3Fy94wTLrPMuytb1JfJhpif8TyPL3oWz2Sw7anmY0WiUTZs2MT09zcMPP8wNN9wAwA033NAIF9+zZw+veMUrEEJw/vnnUy6XyeW6I1z1xVAqlXjggQe48MILF9x+9dVXs2fPHvbu3UsymWTDhg0A3H777Tz77LONnsaVOdWeN2/ezKFDh3jmmWcW7HsfhmGLoJZScsEFFzQiDw4cOMDv/M7vVFdXgf379zM1NXVa9nkxfv7zn/cE5WniqaeeWvYzmzZtYmRkhGeffZabbrqJRCJBsVjE931GRkYYGBgAYOfOnRw4cKDxvXpESY+V0Sz8JarkpIX/+MQEWTHN4/7VbBPDBO7yAtCyrI4phikfehCef46j2gVsvfXly35e13V8IXCiFs8Wb6IQJLnnkW8wYU+Qr7Te89aK0dFRhoaGqi9sm3FNg/xWKoa34lD/crlMJl7BIdpVOf5PPPEEt99+O7I0u4glkYjIymaCqVSKou+jBRqu077CH6AcSCIBzTn+EYm2TJ2HaDRKIuGxcaeORHTVwg8ApRIhCnpqZYs9UO3hvn2HSbFUwr7yBqSqEfXBiqy8bspqYFlWs8Hie9XFLX1l4xyqLbwfDneyvhDhvmye64ZVRo+3RnF2Gk3zz0IBH51IevFWfnVUVcXzvGpxN0C2aZeTeo2kBrWUloQoIHLnorO08O/ri6IoJSJxhYqMgufxzRe+yZ7xPZTcEu998L1neA/OHIVCgUi9HXlsmUquC1A/d7YN2szITK+q/2nkpO6g4+PjHDp0iHPPPZd8Pt8Ia81ms42J5/T0dENIQDV8dXp6uvHZOnfffTd33303AB/60IeavtMJaJp2UmO+4447+OAHP8i6dYtXsd60aRPf/va3+fjHP95oCwXw9re/HYArr7ySf//3f+f2228Hqk6IlBLf99mwYUPLeOLxOFJKBgYGyOfzpFIpYrFY43PpdJpjx45x66238q//+q8MDAzg+z62bTc+8+STT3L55ZeveD9XwszMDJVKpWks81lq25niZI/pWpPP5/nyl7/Ml770pcZ7juMQhmHTRGTdunVIKZmenmbXrl24rsvevXuZmJjgj/7oj5r22TTNxut8Pk8+n++o32QhVuu4ep7HBRdcUL2OFAUtlGQHBtBW+H9Ho1HuvfdeBpRp7vV2c776LFTclrHX84nr1CdJ7Xyc6tezNVxtTzr6srew69XnMzCwvKMhdINC+gR9L7waS3+WXxy/l4+/7rt84P4PtM0+F4tFrrnmGgYGBgiOD1NSTXQrQ8V0iQbLn3+bN2+mUCiwLitxgghxVSHWJvv2YgjDkEwmw8DAAMcDG901EAiseJH4QP+C+7jQ9arEYmgzFlK053leP79tKYn4If2DQyi1RcAwrLbtGhhYXPDs3LmTeLzIOVdsBfYgnEpb7uepEIvFiNfiPKID60iucL+uvx6uvRb+4R9ivPZPtvC9G0Z4xd+vw5Lt9dtEIpGmFM5iLcQ/ns6s6Bo2rriCu8Q9TMkBsoUEP98a8MGfGAxvmWqr/VyMpZ6vc+dxtgxxpUHfxuSK9uvSSy/FPnoQAcQ0lUQb/hbj4+Ns2rRpdh8BV5qkRAEDF52l71cXXdSPph0lMxBnnCi6LDITFjjhnWBcjrN3Zu+anQMvdt4UhiEZXQcJ8fXriZ/k30qlUqRSKaLbo9hPx4mGwYrvHT2WZsXC33EcPvaxj3Hbbbe1hI/PZaHQlIXCuHfv3s3u3bsbrycnO6uoxcDAwEmN2XVdhBBLfufNb34zUF08WYhkMsnRo0eZnJzEtm3CMGwIPUVRmJiYaPqt6zn8Y2NjvP3tb+cjH/kIuq43xtDX18fdd9/N61//eorFIpOTk40x1j/z3ve+l89+9rMr3s/5PP3004yOjjYda8dxeP7557Esa9HfY6ltZ4qTPaanizAMsW2beDzOF77wBW677TbUFTjFe/fuZf/+/U1j/ta3vsVTTz3F+973PqDaRs3zPDzPa4j/7du38573vIdXvvKVbNq0qen7c3/3ZDLJ888/33HX5nxW67gePnyYyy+/nMnJSRzPR5WQKxQQJ/F/T05Ocu4NlzN993oEe8FzmTgx0nA+pqenue222/iP//iPxrU+Pj6ObdttfZzq55U3ehxFwpOF7VyfnGRycnnh7wuQAs6dkQzkbuJtfU8zfuSvcJKPMbHjDxq/zVpy4MABXvOa1zA5OYk8fBiHKClXUjIq+CV/2WNTqVQYGxvjvIiDU4rw1n0f4aOjVxHRVu6QtiPT09MYhsHk5CTThUkMN4UiFax4kXIQYi3wuyx0vZb9AMXXKBRzbXme18/vUiCJhgFTpSJizlzoD/9QLHmux2IxLr74IWa4CIFE2lbL87wT8TyPSqVCaWwMAdiqSuUkj59lWVx00QQ/+1mMQ5WXYImHmDhxYsU59Gea+XOVsFaQuVypLHh+L8TeK3cQ42Vkn5oiF5GcM6PwkD3Rluf6fJZ6vpbL5cY2OTJCgIKMqivar2uvvZbHf1Atcmjl8zht+FscPHgQTdN47NBjfPW5r3LusVEsQxKjTErMoAlvyX2VErZufRxhGDgygmuViD72LEcSwwTZ/Zx7oMD+w8+RSay+4H2x86ZSqUTBnkENVSzAPsm/pSgKhw8fJitACRWKUxMnfe8429i4cWWdE1aUcOX7Ph/72Me4/vrrGznq6XS6EcKfy+UahY36+/ubTpapqakWt/9sw/f9Jgd/MeorXEuhqipBEHDixAmGhoaQUmIYBtlstiWlQkpJJBLh2WefZd++fYyNjTVSCAC2bdvG8PAwqqqSyWQYGxtrEZyPP/44QbDyvpvzmZqaamlVuGHDhpY2g2czTz31FJ/4xCewbZs9e/bwla98ZUXfO3bsWMv5cvDgQa655hp+9rOfAdWJ9/xuCZqm8fd///e89a1vbfmbyWSSfD6PlBLTNBsFJ3ssTy6XazjxHgJNypMK9a+T/fPbyLziCrSYho8C+dkw/r1793L99dfzox/9qPGebdsdE+pfLE5Rtofoz/rE4yvLX9zY14fmRthYVNAKQ/Tf80v40hfwHnoQHjiz9UhWShAEja4FFAr/P3vnHRhlff/x13M747L3BhLCBkWWA2lRK2qtv5/bWrUWrb/aam21rjrbqlWxbhEHioqIC1G2jDAjYWWSvZPL5ZK73N7P8/vjyEGYmQiW11/k4e65783n+/6M9wePpCbSI+JWeZDJTyzeoqKi2L17N9pwNxaVnGpjBXV1u4Z41UNPe3t7MBtqd1lQedSo3BoUPkWve/wBfAoFCp8Sl/fULvd0IhHi62nuB5zws959TXTJ5SCTEW73YbGe/pvc4Iz7bmPHcG2/zzV3roPPfbfjEwQ4lct+fT5A6nWPP4AYI5E2IRq1R8MkvYxax1lYvbahW+OPgN/ShYCAoD3+Hreb+Ph4zAdanvKEOipNP/746cPprqRt6KpjmjGCs1cXcW7eJQjx8WhllhOW+qtUEBenQ5MSh5sQdPoq0r7/AbZsonnLN/zy2yr2bFp0kp7N4GN1mFC5NSecaHI0wsLCsNvtEBaGyqvC7jx1WvtOd06oRiVJYv78+aSmpnLFFVcEj59zzjlBd/i8vDymTJkSPL5582YkSaKyspLQ0ND/euHf3NxMWlraoJxr1KhR7N+/Pyj8U1NTyc3NZdiwYUedoBAXF8eGDRuYPn06paWlQQOPH31AAAAgAElEQVQqCLi4d/99xRVX8Oabb5Kenh78f5/PhyiKAxLpNputR5+4JEnExsae0EdAEITT2tikLxQWFtLR0UFBQQE333wz0dHR/OlPfwo68R+LpqYmRo4cGazs6GbOnDn88MMPwMG+c6/X22PkULeT/+GMGjWKyspKOjsPlhk6nU4+/vjjgTzF/wpEUQwGzryiiKKP5n7dREdLZA4T0Yb68EpqsBx0dy4rK+OOO+5gz549wWMncwrHQLHaO6h0TOPWS6p7fZ9kSSR2/89IF1p6HJeAtsOCiqcEFjMuSUOM14NH5YZeBH21Wi333nsv+6uKaIs38H95bqoW/vskLHZoOVT4Wz021F5VQPh7VdDLHn8Ar0KB0qvA5XFi9Rzb8PLwsbgnE0kUcQIhoq/Xo9y6SUhIoL29nXfefRd/aCjRLjA1lLG8ZjkARpfxtLweOhwOwsPD8dssCJIA4X0XADKZDL/fj0wG2aGNAQ+MU8jk8YiqDF/AuLgvwl+r7WLCtMC14vEtKt5z/QlcTqQBJF1ONazWDtQuDZwgudUDhRIJidWqGipMp57ngdlsJjIyEsdL/yLyhZcYVtqCwq9AuOlmIrITUL49/4TnkMlkqHIzcEkhKMxWJrXJweMFg4GJehlFradvANjisaByqyGs7z3+8fHxASPqsDAUHjUO1+mR3DgdOOGOpKKigs2bN1NSUsIDDzzAAw88wJ49e7jqqqsoKirinnvuoaioiKuuugqAs846i4SEBO655x7efvtt5s6dO+RP4lSnrq6OYcOGDcq5pkyZwq5du2htbSUlJYU5c+Zw4YUXMnz48KMK//j4ePLz87niiivYtGlTj4x/bGwst9xyCxDwF6iuriYnJyf4/x0dHUyaNCno+N8fbDZbcMNSXl6OxWIhKioKh8OB5jgZn26zq/8G2traOOuss1i+fDmTJ0/mV7/6FTfffPMJR2GaTCYmTJhAY2MjTz31FFu3biUxMRGZTBZ8zY1GI7GxsURHR/d4b49Fbm4u+/fvp66uLuj2v3v3bgoLC4NTJyCwwW5sbOz/k/4JcugG0CMKKESpV6LvcOLjRa67zkF4uAReDQ6jnnXr1rFz507MZjNRUVEHs8sQbPU5HbA4TIS6Vcijep/5U7pcqMquJEtWiyImAuvo6ZiuCFSr5K/98YTeMbFYcKEh1deFR+Xt9WcgNTUVQSEnd/8ELq6VU6srRu/QU2WqGuIFDx3t7e1BX5tOtw+tR0TtViP3KemLzXMw4+9z8sSOJ455u88+O/njHr1ebyDg5/HglMsJEWR9LtGPiorCbDazd+9efFot0S6BqvI8PtjxMpIo8vqOFzDaTz9D3O4Z9zZnF0qPul+Zv/j4+KAZcLjGg0dSndozvX0+QOhT8CcxsZmfX+xHJogkWuWU+ScE6sC7Tt+RfodXunY5OtC4QiEistfnUIaFgQDKmnqa3583FMscEGazmciICBxNNYR6D/nOxyUQcXY2qsmTTniO1NRUjOEKHLIwLqqTk2MSiHEJ2BUiGr+Ax3j6fe8hsB+yeiyo3Zp+Cf9Zs2axevVqvEoVKo8K+0+sAubH5IQ7klGjRrF06VJefPFFXnjhBV544QXOPvtstFotjz/+OK+++iqPP/54cJyJIAjMnTuX1157jXnz5jFixIghfxKnOnV1dcHJCAMlMTGRurq64Pio6OhoQkNDSUtLo6kpYJxVXl4OBN6LhIQEXC4XY8eOZfPmzT1MaARB4Lzzzgv+/cc//pHc3NzgpqWtrY3JkyefMPN8POx2O1qtFqPRyIMPPhjMANnt9h4Z6MPRarVYrSceZfZTYfbs2TQ3NweDIRkZGT3G7gEsWbIEl8uF0+kMtl9kZWVRV1eHSqViwYIFTJ8+HTgoQruF/wUXXMDZZ599wnUkJSWh1+upr6/vIfyffvpp8vPzAdi+fTvbt2/vkXU+Q0+8iAdK/fvuQK1QSIwe7UOrFYmwRtBmaqC1tZXly5efllm/Q7G4uwIbgT5s/oQ/3w8KiYynb2fM09fxQs7XvFZxPQYxEYeu/0HJwWa3fjcdzg6wdOGVVCR7rEiS7OB4r16g8noZVzg1sOGTw3dV37C2Ye2J73iKYjAY6FQGqrsMfolor49Ij4joC+uT8PfKFSh8Clx+FwX6gmPerqio6KR/R7qD2QHhLyO0H2353RVuJpMJT2gY0U6BFdvfI7a4GumVebSsWkzz8w8N/uKHmKDwd5kDJb/9yPgnJyej0+kACA/14UF9apf6e/ue8ddoNHR1daEVLJilaFr9qXhQgHFoJywNJS6Xi5BDvuNdTlOfM/6R8fFIwFltcmxt9aecs7vZbCYqPByH3E++aw7/vGQ/TJ8Bl/yCyEjxhNM8AIYNG0ZN/X50UggX1SvY6bmA2I440iwyTGI0smN4fp0O2Ly2fgt/mUzGbbfdxrpt21F61Ng8Z4T/YHF6pIlOc47WZz0QrrzySlavXt0jY65QKHA6nTgcDu644w46OjpQqVTExcUxevRooqOjiYuL6/FDfDgzZswgJCQESZICs6j1eiZPnkxLS8sx79ONJElH7Qe32WyMGDGCpUuXkpCQgE6nIyEhAYfDcULhb7FYeP3110/42KczTqcTtVpNamoq//73wdLexMRE2tvbg3/7/X527tzJM888w4MPPsiyZcuAQIBgxYoVTJo0iffffz84LlKpVOJ2u+ns7CQmJoaxY8cGR80dD0EQcLlcLF++nNTUVGJiYmhpaSEkJAS1Wo3X62XLli08+uij1NXVBe/XPaHjDAF8EgdK/fv2E9s9ahEgIgpCrdHozI1YLBYiIyN7ZPpPR6xua583f8LoMXgnZaIfGc2lczz8819WHr9uBw2ucXgdlh5Cz263s3Xr1qFY+gnZk/cRn27+D5LZAkhEe10gKqAPrRjlk6dgiBnF3+yvISFgyF+HvejYQvdUx263c3/+/Xj9XoyiRLTHS6ZZTnLVWT1m3Z8IUaVC7lPSatdhNjThLT+yxcPlcuFyubDZTu4GMejtcUD4h/VifOPRaG1tZeTIkTg1IUS7BPYk+RnZKUN8fwEuuURL2/5BXvng4xN9lHSUBP/unnFvdpvRuDTQjx7/pKQkdDodbrcbbZgft6TG12Xucf35MTk80CR1l/r34bc6JSWFJ598kijBSI0/h2HyapxSKHSevj4PTqezp/D3dKFx9i3jH5OURKQ5iplNB1rmWo6ehPL7/UckSk4GZrOZCJWSFnkMev8o0sdpaUueihAWzo03OnoV+xk+fDhvvvkaVk1gP7zG80vUjefws/IYXnE+BF0mpO5g0mmE3+/H4ncESv37Mc4PIDs7m2ajEZVXicN7Clf5nGacEf4nicF05508eTKvvvrqEcevvPJKfv/733PTTTeRn59PREQECQkJwXGA1113Xa/OHx4ejs1mQ6fTkZWVhasXM6UbGhp46aWXAHoEALxeL2PGjGHNmjVcccUVbN++nfj4eMLDw4NVIkdDq9VSWFjItm2nhnnXUFFWVsaYMWOAnn33h5bru91uiouLueSSS7jlllt4/vnn2b9/P4IgEBUVxY4dOzjvvPN6zJPNysqivr7+iNFvveGxxx5jwYIFKJVKUlNTgx4dY8aMobS0FEEQUKlU+A5kMiVJ4q233hrQ6/BT4NANoAdQSGKfM/5JSUnBgI82Ro7aEofOFtj03nTTTcyePfuoj3e6YPHbApm/yN5v/gDuuENBfv6O4N9CVCRql5rIKE2PyqB9+/axevXqQVtvb9FaLdhXLaNz2cd4TAYESYZWcCBzh/epH1k76WxmPJLMxFwrZimCkPwC2LwJqV0/hKsfOly4yIrIYlv9BkxKJXGCSJToIN6uBH/vKyFCo2NQ+BTURouc1SKi//6rI26j1+sZN25cj4DpyaCrq4vIyEjwenDLBUL7KfytVisXXHABbo0SrVPO6E4ZOuskjCEgmTNp8p365lbtjnZW1q8M/t2d8Td5rWhcIf3K+KekpKDT6bj55psJDxfxosLQ2MADDzxwyv0G6uw67H4XclHWp4x/Tk4O06dPJ0owsd8/jrGKInBrsRlOnHQ5lENNX39sDhX+Vo8Vs9cW+Az0Iegbm5zMuKJz2ND1a/RiEhwYB3s4HR0dfPHFF4Oy7r7g9XpR+v20K7RMUVdxww0Ohg8PVGMOH+6nN9v+7lZMDiRm3Khp9Y7EbB+JXkoGUURqrB/CZzH4dI9wt/gd/c74d+NVqVB61Nj9p4+X0anOGeE/xNTW1g7IFf9YZGdnH3FswoQJ/OpXv+Kaa65h+/btREVFIZPJgoZ9d955Z6/OHRcXR2dnZ7BMvDd0dHSwc+dOfD4fN9100xFrzc3NZfz48axfv56EhAQSExNPmPHvvu1PmerqanJzc4/6f5IkUV1dze23386WLVs499xzyc7ORqPRkJmZiVYbyJ7ccsstR7j7Z2dnU11djSRJ/er/7r5gjx8/nl/+8pdAIOC0ePHiI9bb3NwcLMX8b8XpdPaowPFJHCj179trf+jEC22sErktAZ2zHUEQSE1NZcKECUCgNLQ7IHeqbX6PhoRETVcNZp8zkPnri8ETcOmlKroO7XeNiELtDiEkUh3s/4VAqffJ9jvw+/2EeDy0yeK4Yr+WFw2fM7x6FGGCHZkrok8Z/8zMTNTqEkbnugnpGMbPGuQoRXDV994M8VQitrWEaxcWkFewhIYoP7EKGVrBTIjg7FPmLywuDqVfQU2UxDmtMlqNR2Z79Xo948eP7/F5OBkYjcaAEarHg0suI6wXUxyOxtSpU5k8eTKeMBGFM4Ibd6Szx/i/NGtFDLax6AQB6VTubQc6nB2Y3QcDFN2u/m1+H9FO+tXjHx0dzapVqxAEAY3Gg1tSYe8wMGHCBDZt2jR4i+8Hh//2flu6lH2KNgS/vE89/uPHj+eGG27An6Sm3D+WsfIiVNZY9J29r2qQJImnnnrqlDF7NRqNwaTDb9f+FpNoC2T8e+nqDxChDlQFbfRegkmKOabwN5lMPa8PJxOXC4dcRqRCICQE/vCHvlUcCYLAwoUL8SYk4hbUJA7TYBJjqPNnI1dApEugq7JwiBY/NFRUVDBq1ChMog+th35977sZPn58oMf/jPAfNM4I/yGktraWJUuWcN999520x7zmmmuIj4+npqYmkIXoB90jGftiGtY9H37x4sXEx8f3mAQQHx/P008/TVZWFh0dHWi1WpKSkk4o/CsrKwdtGsKPjSRJwQx5fX198Hi3SeOx7rNhwwbuvPNOCgoKeoj7q6++Ojhl49577z3ivsOHD6eiomLAY95SUlIYN24cEHgfd+7cGfSFkMvl+Hw+SktLyc3N7XOA61TKTgyUpqamYIBtdf1qvJJ0oNS/bxn/tLS0oKdGREo4bm8MbnPnERvMyMhIzOZTPwPYTXpDCa+8eR2dMhmxohdCQvt8jujoaObPnx8o5Y6MRO3WINNIPcbHWq3WE45EHWwsFguRGjWN/iw6dbN5JE8gUZ9CqGADV1SfhH9WVhYNDQ3kTFQRVzqbcQY5I40yqhtOz3L/tLoCMvVuLl64meGN6cRpIPKhPxH683MRckb2+jwRcXGE+3zURME5Ojkt1iNLfnU6HePHjz/pGX+9Xh8wMPR4cMshrI/Bvm7uuOMOoqOj8StdOKQImtsuJ93moyhRxGvNwCGFwUkOavQVwydvYl75OZK5i2+//Raz2RwQ/qKPOLe/z5U+EBBGSqUyYBQtWPGgxtnZydVXX83OnTuDt/P1wUtjsOge5wYg2Wy0fvI6VZ2VyEU5KPvu76K5/04Komcx9poc5LZE2iy9z/jv2rWL3NzcE05MOlns3buXiRMn0rVtHY79hWyLsRHqVkFkH9q8ps3AGhLG5PAiXO54rM1HD4AajcYfT/g7nfhQ9sWy5AiUSiWKhES+/cNCxvz5IggJoVEaRtpwOXEOgY6mgbX5fFf7HZ9VnDzj04qKCkaNHIlJkIj2eiG079f7bqZdOIsIrx+TICD5fLS0tOA9DVsfTiXOCP8h5PPPP+e+++5Dpep9L+NgoVQq+y384+LiMB5mKHKirGJnZyfXXnstn376Kffcc0/QCK4blUqFTCZj1qxZCILArFmzjpnphoDwz83NRaFQ/CS+5MuWLeP111+npaWF+++/P3jc7/f3KNE/lOjoaGpqarjwwgt5++23e/xfaGgoqampx3y87oz9jTfeOAirP8jf/va34Ji/zMxM6uvrqaioYPr06Ud8Zg7lk08+6REY2LVrFwsWLBjUtf2YNDY2kpGRAcDi8sW0hntQimKfXf0PNbLSnjMSqxQB7UeO04yIiAgGdQRBQBAERFEc4LPoH37xxAGfmJZi6n3t2GRqYjTefrU+/f73v2fWrFmsWLECoqJQuUIQFf4jMrwKheKofiNDhdlsJlKtxoeC3b6pAEgIhAl2JFd0n4R/eHg4drudiNwUrFIk5b4xuNvOoUxfNFTLH1JqYxSkW2RMb5WTVTMKbRhozx1P6PknNho9lKjoaMIkP23hEtbWmbS62/mk/BNabAeFUXfG/9BA0Mmgo6MjmPH3CTI06v639Wk0GgTBim30NJrETLLtdnYniQjmNByEwkkOavQVQ+Ve5E43VFawYcMGFi1aRKhMRrtcRqJfhONM8jkeCxcuZMSIEXjFLjyocB+ospAfMi51/vz5VFSc3JFvPaoi62tROb3URYnI+ljq383Y6bnUm5MZOVoCawp6e+9HKW/cuJFrrrnmpH/+j0V7ezuJiYlUrvuY/9vuZ1eySITCh9AHbw8hLJy288K55l+jCTHHsd1cxF3r70KUAte67n2pyWTqVUvqYBLcE7tceCUlmpCBVd6FhYXxQ1UsZ08DLp2D75JfokyOI84h0N5R3+O23c+/NxhdRgoNhTTb+m/S3VcMBgOxoaE4BBURShFhAFV4sXFxRIg+jIqAqeenn356hL44Q984I/yHiPb2diIiIo5rpjeUjBkzZkAZ/z179gQFd0JCAnr98XtMu0f/zZs3j9zc3GNegJ999lkgUNJ8vB7/mJgYbrjhhmDbwelOSUkJXq+XRYsWMXr06F6VZ2dmZgbHL/bnc/SXv/yF0aNH9/l+x+Oyyy4L/jsnJ4eysjI8Hg/p6enHzbQVFBT0CAysXr2aKVOm9LhNV1fXaTspoKmpiYyMDCS7DX9FGRXxdpSSBIdsTHuDQqEIBkjUo7PxKMLAYiHUfXBT4/Q5g+O/ILABCQsLO+b4S0mSemXQ2V/eKXkHg+PITOSn5Z8iSiJ+v58OuQOZKQOLXE1UeP8DeaNGjQqMuYyMIsSjxCq6gxtdnU5HYmIimZmZJ3XUpNlsRqtU4kcBCPCLOTBhImHYEF0xfRL+cGBDOTwwDWeF539o7vgZ9daTb1w1EOx2O//5z3+whylocgTaU2xSBOFTR5OR4WfmTHefzpeUlESMx06YW8FCywM4XBb2te9jZd3BfnKz2UxmZiYmk2lQn8uJ8Pv9AdNNrwe/pGAgcf6Af4ob3W1Po7juGlI8fvYlCCTaFAcy/oMj/HU63ZC0IHb4zcQ5BESTkbS0NN566y3UbjdWhYqEUKHfXkcajYaMjAxsHjM+SYXXbD7CMLmkpOSEI3AHm87OzoPCX9+GQgSXAuR+eb+Ef1SUhFLpITJNGxD+7p4ivtFy7N81mUxGUlLSCfdL7Y52NjVt6vPa+kr3e11hrUXbPJpr9sWiDen7b392dgna7DgiLFHMj9rPnePvZFHZIubPn88zO5+hwlgR7Ck/HFEScfqGpkRcr9cHWlFdTnwoCOnPOI9DCAsLo6VFRkKCiEEmUGxxEJ2sRm2PwmBpxelzIkkSpZ2lPLnjyV6fd2nlUu5Uno9Yc3LbxQSHHS9KwkIG/jsTIXnpUirBYcfr9VJQcHpWwJ0qnBH+Q8TGjRu59NJLf7THv/HGG4+bET4eycnJzJo1i1/84hcAjBgxgpqamuPex+12ExISwpgxY3oY0x2OppcR/5CQEGbNmkVCQsIpE8HuL0VFRUyYMIHrr78eURTJzs4+YSAFYMqUKYOesR9Mxo4dS2VlJVarlfj4+OO+T3q9PpiZ7e6JjYyM7NGK8Pnnn7N58+YhX/dQ0D09wbNxHeNKO6hOcCCHAUW6BYUC4hPwymCdcgWbWzZT01XD3RvuJiIiokep/+Gv5aG0trbyyiuvHHFckiS84sCraVoai+loO3JTkd+WT6ezE7fJRG2ICiqvoCbWQ6R2YCW5SqUSn0pFgteJXqaktjMQZNywYQPTz51ObHostbW13L/5/mA1QkFbwXHHwA2Erq4uItQqJEkgfkwsnQ++huz8CwgV7CiqZvfJ3K8bKSEBLr8S/wU/xyWF4beaTwsvh252797NtGnTUPl83GN/D6cUgkFMIOJPtxMSIpGV1bfNYGpqKhGii2hLGMX+s9CF+hn93Q4Muzb2uN2h1x5Jkk5uFYzHgx8Fqv4ltYMolU4WfpbAHQ9qSIlxYlPIyLR5cfu0uNsHFsDbrd8NwKJFiwbsir+5uedvteTx4PK7CPGBqaGRtLQ0xo0bh2Duwi1piIoa2HuhVCrxyOVIgAUrKxsPBn0+LvuYhMSEk+703yPj39aGS9LgkQnIxL71+HejVEJcnAFPVBRKjwa7s4sWWwt5zXmIksjdG+8+7v1jY2OPKfybrE1YPBbeLn6boo4idrbtPOrtBoN9DfsIiwlDkiR0Lj0fGp7if3YOIyKk75VYkyZN4sl33yWmI4GHt8g5K24SZreZRd8uQr9vG9t3fEK7qR1XfCA43tLSQpc7UPa/tXUrT+x4YlCfWze1tbWBMd0uV6DUv//V7AB0dYWhUHTvC5vR680kDtfgtyXT4Wjn+V3PU9hRyObmzShkCjodB9/nY/3OSZJEh01P7K13IKxdhXSMqQgDpdJUyfr169m8efPBaju7HQ9qwkIH3oITpnDhElRsa95y0iv6foqcEf5DxKFz0H8Mhg0bhlqt7td9BUFg+vTpwbnv3UZxh3J4Ru3wSL5KpRqUjEJ8fPxJ79kcbPLz87nwwgvJyMjg0UcfJScnh6qqqkCmUHvs8UbR0dEkJyefxJX2Dblczv3338/9999PXFzccd8nn88XDAzs3LmT6dOn9+hn9/v9tLe3/yh9moOFIAg0NBWS2ynDLwMVgyDUEpO4vFrOn/fGsbV5CyvqVjApfhJOlTMo/AVBCI6/PBoVFRXB9gGH96AIXd+0nrcKBzaNQdK1ot/yHcZX/3XE/xUU5bO7aheehno65OGIjTMxqyEqemACYMqUKewsKCBBctOuDGGdZh2ttlZK6kpY1L6ILZ4tmHdso2rb1+xY/SZ15jpW1K1gV9uuAT3usejq6iLsQGXHnBGFvPNOGJmZPsLUHkLrLujz+UaOHEl5eTkpU1M4/8aAuenwJhu15oFlM7vcXbh8J6ccVqfTkZGYiOR2kysv460R7xN92/+gjOj/7jjK70RlTiJbXoEuRMHFW9pIX7+LWv1+JEmiUNXTAGvLli18+eWXA30qvcfjwY8MlWZg26rExCbeecdEVJREUqKPqI5kxvqaUFkS0fXB7O1w9C0VvL38Id7fM5+WlpYTBvOPh8vnYknFpz0PGjvxSXJq/dmYGuoDogjAYsaFhujogU828h4YkdcYYmR9zeqgCFhSsoTMiZk9qp4O7f8fKroDvgBefSvlvvG43QkBf5d+ZPwBpkyxU949qcRqpaCtgBV1Kyjf+iX+ynK6So8dwIyNjcVoNLKybuURwn5x+WLeLHyT81PO50+T/sSm5k39Wh/AkiVLjvv/n+36DPkIOXR24nf72OU7F4sUidbc98qliy++mIf/8U/kYhiTGySkX1/LL6Qp+GabuWtxJfp1X7Jf2k9xWDGSJHHV21fx8KaHqTPXsUe/h9ExoynpLDnxA/WRuro6hg0bBk4nXklJSNjAvvd6vYKcnEDFoyhWER1tIik3ArsjDbPHjIDA+sb1mD1m5o6dy9w35gbve7RAXqWpkq2tW5nQcsj1tv7Evx+FhsJete8dyhuFb1BYWcj333/PE088wfXXXw8OOx5JSVjowPdBIRo3blQ8WvxvXKI12GZ6hv5xRvgPIYM5wu/HJCEhoYeo+/DDD/nHP/4B0CO7cihxcXGDkqmPj48/6S7Ng43FYukxUi8nJ4fq6moaGhp+1ODQYNE9NvJ47/ehFQGlpaWMGzeO9PR0mpubcTqdvPTSS8yZM+e0/M7YvXaa5YEARrWxgsjOeDI7wlH283qnVquDzsxFej3jDXIuKKkgYuX3mFwmbhlzC5u7Nvco9T+05/9wKisrGT58OH6/n9vW3hbcBO3Q7cDhCwQCfGIg4LK3fS8Wz9HPU9JRgt5xWKVKXR1+JExdrT0OSw31jNS1UfXuC/iaGrFKkSTZZESZYogcoAA499xzWbNmDTEKB+1qFVNqjXz60eM4ch389ey/olQoSNi1iuv3iWxcPo93S97l0WmPYvcNjSO62WwmVBYQ/ilxDh55xMo11zhRhSpR03ehPWPGDH744Qd+/WsH512iQlKrmVnhI69yVfA2kiT1uQLgyR1PsrklkKXtS49ob/mg9IPgv3frd7Oo7h2chDAlupT23J9zy18GlhILFxwkFVzDeYo8rtk6mlSbjFk1Itu2fECzrZlCdWHwNSkyFLFt97aTO9vb48GPHNUAevwB5HKRkAP9wkmpELv3VyQJLUSbYqi11gNQZao64Xk2NG3AL/qp6ajg7d2vsWzxgzz1bh3tW1cSExvTI5jf189S28L/oN+2CqnukGBUZwc2SUuLmIa1pZkRIwLtKhzI+EfH963t6Wh4lEoUXiUmsZnYFetJDw/DYDDgsDoIzQoNXj8kSeLe1fcOyef8UA4t9Td01OGzZqA0pqMUpX4L/4cekrO3phZBqQCPh5r2MqLUUeRv/Yi5+X4K1y484j5OpxO1Wh3oE3f/gFKmZG3DWlHJygYAACAASURBVERJ5P73A55CgiDw0JSH+Fn6zxAEAZnQ/+3/mjVrjjs9oLGjEbPGDPV12KQIUmWNNIjD0Pr6tycMCwvDkq6iPWwElBQjvjGfd0wzGWWUIdjtOF11zNBHMW/n89zSoObvT+exZtHDeHbv4NefVbCqduWJH6SP6HS6QGLG5UJEjjK0f+93Nw89ZCE0NBDwiY+vZvz4EhIylRjUI3BLPrQ+BW6/m1BFKLKv1pDVsB/JFGifrKqqOiLx8kHpBxTp9zL7uzIAZBL4Gg5+X1fWraTJeuSUhAXFC9ip733QTJIk2uxtNLmaeOyxx3jsscfIyMhAtFrwoSIsfODCP1ILFUk2LtveSVTLNqZMmXLatoWeCpwR/kPAoVHgnwKHXkwXLFhAYmIiM2bMoL29nSeffPKoZetJSUk9nP37y4kyyacj3UGR+vp6MjMzf+zlDApH6zEXRZEtW7bgdrtJSUkJBnB8Ph8KhSKY8X/77be58cYbgxUmpxsGh4FiVTEAdfZGvmp9goz2SBS+/pXRp6en09LSgsfjIb+1i+/P/zcmRRRXr27iqg9+IOK6G8FtxWw+WP59POFvtVoZM2YM60rWcqPmXBYXfcAHpR8wvNqIIj8fu9vGDStvAGBJxZKjloBKfj/bX/4TlS8/HPi7Wyh0tONxpNDmO6xnu7SEVCv43O3YKsqxSlqyZLVM+/4aIoWB9WArlUouuugi1EoT5Ul2rt4v0FG+lfjUWKL+9giKDz+gLcbJRL2cWCf8TnsRig4jkq1vY5Z6S1dXFyHdWu/QVqYJE9EKFkg++tSOY5GQkIDBYEAQAr+9sbESKns8DfW7g0Gbl/e+zLrGdb0+58amjczOmE2xoZh6fT335QUmzSxatIh/5P+DOnPvM8llnWVHPf7R/o+QJAm3302ZrIw/x1zFJXuGERvt5fnnzYSFDWwDGIqdtrZfcK4yD4V+HKIkkGqT0VKxk1VFq5ikmUSFqQIJiVf3vUqNVDPkpf49BLPHgyTJUagHLnBdLhdLly4lPlODcf8dJKg7iDUkU+5tQe/Q8/QPT59wTa/ufZU6Sx17nr8bywdvUdm6j0SHjKTCauQhYvD3WhRFnnzyyT6tT1eyHZ/kh32BzffahrXo2iqxSVq8Pi1eq+ngHshsxo2aqISBmxyHxsah8ioxaiSG671EWBqpba0lxh6DQTAgIuLyudhWvw1zu5lPyj8Z8GMeD7fbHWxfbLU0E26Jwtc5GpVfCtTt94OEhAQMHR3Bkad+cxdjYsaw1V/NxXVyik1Hfv86OzuJj49HEAS65F1cnHkxCaEJvLj9Rb6p/wa7x46yogrpi88Q7/sj4m9vRnK7ycvLw+gy9jnw09HRQXNzM1WmKorbi4PHK4yBtiuXx4WgFKiqzSfUlMz5yk0U+84iIrv/45nNI0NYO+ceADJ272T85r0sdt1GXEcs55bV8Ng3JbStWcrde9pJtvhoKc9HvWMniq+/Qqge/P724KhklxMJCSF0YH5e48YdrHaUy/3k5ibgdNaiD8uhLE5k7L/f5RfLSrmkXCThxWdJdrlgw/dAwFOsszMw/cdgMNBia6Hrm23836PfELKnkE4xDq8lA31LOe+//z4A25s2s7jsIwA8fg9LK5cCkBaexpaWLb1e99NPP01KeApGmRGFQoEm5MD3wdxEqCWGMO3AkzlRsQqcSvi/3UostJGVlXUm4z8Azgj/IWDXrl1HGJf9FPjiiy8YO3Ysl156Keeddx55eXlUVVVRXFx8RKZ2sIR/SEgIbnffjKBOdQRBwGazsWXLlp+M8D8aX331FYsXL8ZgMDBixAhsNhsWiyXY3hATE4PRaMTlcp22YxvXrl3LZ3+5G4evEdHrxWEz0eIew9Td55Bo6V+rTXp6Og0NDZSUlJA9Ukf7edN4KHQ+gi2J8durobYGWUkJPr8Pl8uFRqM5rvCHgNnn+nWv8Yu/vsFDf1/LzJVlXPfv7xi/rojnvvoDWXUmWhqLCVeFU9xRfOQJWltoNtbSXrgFv8/HvHnzAJDa2+myZ9MiVyEdmgEytBPlEvDK3egK9+IT1eTK99PqmEhIl65fr8uhzJw5k3HjkzCH+JiskxHidnH+plrYtIFxjW6+TTOTbRK4a4+KrF//Hmn2BbD00yER/x6PB2V3W5P6oPAX/vEc2uQwhHc+6Nd5u0XriAsSqfHn8PfFbWxv3sr8ovkoOozsq9h4xH2OtYHfodvBFV3JtJWX8vqnz2BuqcHj9/DhVx+i79KTr+u9S/Jj2x87ohTU4/dg89potbfyRdUX/GGHC82tt+B1phIfPzjiOyxUpEVMZ7ymlGYxg2ec/2CXdypCYwN71n3C8xu62Fz0FdY0KxNbU3Cpht7kz2w2HzTR9Qb6TgV1/wTfobS0tLB06VKUqUlYpEhiRoai8qixuywUGgKVDaIksqx6WY/3otPZyU2rbqLV1EhGhZGirUupN1bz5zwvT21S8oT9eYbp3GiNlcFrdmtrK3v37j3qOiRJIq8574jjepeBJLsAB4L+m5o3sVm/A7sUjuiKodMSCNZbPVYwm5EkAWVM1BHn6SsZo0ah8CnxyGGcLoRWRzmFrYUk+BJw+V1Uh1Xz3A/PsapyFQkVCUfNaA4VOoeeeJuK8MZJDG9J6lePfzd+vx8pXBtoFtuwjvNeW0Zkh52Vtl/jMB9ZAak36ImNjcXpcxLq9iO++BxXrW+jsnIft+iSeW/53xn92Xqkpx6D79fCrp2E7ivhzffe5N4v7+Wx7Y/x5I4n+ffO51hWduKxb+Hh4TQ3N1OgLyCv4eDn47ldz/W43ff6LSRXT+LcKyMoTryciH890u/XJCPDz/IiH5wzhVBRBKORLb6fE19xHrcWKVH7BZ7/3Bq8fY5RYEbTAYmzb/fQeaR0TxPo58SKQzk0yTZ27FiqqkrwhsUgAGe3yTnr2wJGPvMmoiSg8w7D2VIPBNpCOzo6MJlMPPz4w6z/7mX+tr0FmptgRDbLJz5Pk3EmjY37eLvhKb7Me4tJ73yLdsU6qruqWbjrDfLyP0Fv1ZEQmhAw5e1Fub8kSaxbv44MbQZWmZVNzZt4riDwGaizNaA1JhEWMXCZmRCn4uL1l6DwaJC77MhdriNaiT/66KPgNbP7ve72ejhDT84I/yGgqqrquKPqTkc0Gg1VVVXBGe4jR45k0aJF3HnnnZSVHRmBTkxMpL6+vtdmfsej+8ewsrLytJpdDoHstuwoBm+zZ8/m73//+4829WGoMRqNVFZWMmLEiKDbuiRJFBcXM2FCwOVbEARaWlpISelbRvRUora2losayjmn0c2ez57H43ZglSLo8KajoH8eF5mZmVRXV7Nnzx5+97tkVKqtXHhzI99yU/A2cXvL8XnNOJ1OQkNDiYqK6uFmvqJuBX7Rj9/vRyaTIY8RSa6oQeMXCLe4yFq0DLkkMLVFTnFVHnctbeCrTx4i8bPv8OR9HzyPJEnszfsY6mqxSJE0KZUY6+uDJdQmYzOSLRmrXA3mgxdZs64RtR8Er5e0KIFwawTpsgYa/VkQ3/+sz6HE+doZUT6RVfYb+Uu+kgs+3QbAWXo5Jo3Eg5b5mKRDxIbbjVQ1uOO+3nvvPQAkVyDoIYQcIvxjY4kYl4GQmdXn806YMIHCwkDP+vDfXUht5FTkNTXcsUfBGH8ctz+4BP/yL5EO2/y8V/oelabKHseMLiNRje1It95E9LYtCPXbuHVxGduWv4o4yc3dS3Q05q+g0lTJ87ueP+66PH4PbeYmmkw9KwSa92zgwlIHlQUraGkp5dKigAdMhxhPXNLgbDPCP5hPSIzAvAkjsaljEc49j68V1xJvk4gw1pO4t4Ky1R8yIi2aO176nFG1lURGRAypy7/BYAg4e0Mg4w8MyNb/AC0tLWg0Gpw/u4i4CD0xj/0l8B82K6Wte7kicgYVpgo+Lv+Yba3bgvdbXPIhv1ZN58GlN/Pnb1qpXbYAO6GUes/C6kkizzebSGM8CncLNYoaHt/+OAt3L6RpalOP0YjdbGrexHsl7x1xvM1vYphJhq09IKwjGtqord2JU9QS4xJJSguUvz+x+VFaTPUACFFHuq73lfTcXJQeFWGmRDa03Ee9u4HitmJSVQEj4yhDGenfbaOps56JYybic/lOiinmmrpVVMmNhFsiEbxaohyqfpf6A1x77bV0ee2EuZUkN3URu2E7z25QsdB1F5LDjt/UyS79rmA/9kvlLxEfH8+2qnXcubEaPnyfuPc+ZsFLu/hrgY7FjV8yUR/4HlpT0wHI2LSX0aOSUFXU8mTqb3k89CoeeHYLVa8+iqQ/ftKmu1qv1d5KhyNQvu/zefmhZQd+j5uchlridhRSa2/E7BjBtJ+rqDCmEjEyqd+vyc9/norbnULtTf+C9AzckoqEUB11nnGE+g4mnmqSJvHHrF1M3jeJs3UK3MowpM5OKDx6cKu/BJNd3QFvzcD3chqNBoPBgFKpJCcnh4qKCrwhkfy2UEGM68DjaSP4JPQ31BsupU6/H6fTSXJyMp2dnXxb9i1b47eyY/9qMiwyvp/6Z9rf+JSWhMmEW6L4TFnGs7vkbPruReaUeLh1eTOfffsS2k8/55dfFPPh0r8y4avtTNWr2Na87fiLJfD7Z5VZSVAHfgMLmreTJI+mtLOUOlM1GmMaYfED1wDaplK0bdn80fYBcp8cZ/EuXIKLb2q+CZq4vrDlBSqaKygpKWH58uWY3WZuX3v7gB/7p8gZ4T8EuFyun5ygmzNnDnfeeWfwb0EQ+N///V9mzpxJR0cHYWFhPW4fFxdHfX39cUf29ZbuC/cbb7xBeXn5gM93MmltbT2qsJ05c2a/xy2eqni9Xh5//HGeeeYZXnzxRe655x7S09PZvXt3cHNcXl7OmDFjgvcxGAzMnj37x1rygLFarbgUMLtOwUO69/j1vlBSZU3oxFTk/RT+cXFxmEwmqqqqmDRpEmVlZSTlhNN+0W3UPfQhr8S8ygi9j7COUpxOJyEhIURHR/cQOAtLF1LUUURtbS1JmUl8vOFZ/viDCCOy2fbbpXjkgX7rCLfAB9+oGNYlsMpXxJTCDuT79+N1BsqAfQsXcPfOh/A9/Fc6nSOoVcXTVVWJyWTCL/rRm5rwWTJwSxroOvj4rboaJPuBzYB+F4m6NDLv+18c4UkIf3u4vy93D2ROKyO3Xsc7rj+h92QjIMD/XEOsU+B3+XEkZqq4K+1NhPcWweQpxDgFTLVHqWboJ263m3fffTdgdNpdlaTuucnRavsnOi688ELy8gKZtLQsGUWjbsMrKZBe+w/n3/M8IT6BtA4vTVU92zIqTZXsae/Z+7gifyFz3gy0BYw0+EG0MaNZzn9q3ucucwS5u4uRtm1lWdlSfFYzFo+FtQ1rj7qu0vUfc9mWdmo+fbXH8cb5/+TnRXYq338WqbYWuxRGpxhHh5RAXNrAel+7CctJIeecGFrVGsqn3sU5N41AkQBZLYlEuQOb4pdWSPzm/95CJfoJ67IyUSFSWRkIhHxW+Rlm9+AGjtvb23sIfwD6MKf8WLS0tHDVVVdRUFlJxNhKNBMn4tSoUXtELN9+xowHXua1tX/nD3vUbNkdKNE1OYzYv/2Sy+57g2k7Gskyy/ALoBeT+MD1e3Z6z2NS2L8o7rwCq9RFaFcp163WI5VW8pB+Kq9ve7HHGkRJZGPzRsbHje9xXHLYseGm03Au7aYmfvjqQ2JWbcSha0BwxBDtFvErfEgN9XRtWE5ewWJUHg2yQRD+yqhoVB41ofoc6v0jyWjs4gdDPrNSRqPU6TmnuIVbv6vnD6u6mJ2ZgcwhYHQZT3ziASBKIptq1tCpkBMrk+GVFCgFLwxgokt2djahYW1EdKQwWRdoHbH7Y9GJaYxrU7K3cCWralaR15BHnaWOWkctcXFx7N33Lec29mwx0/gFriuRkeiQ4XvxFV6adj51qelkdHiJb8lnWl0rsl/OgVtugOoq8Plg/9HbeQAcDgeZmZm0t7cjSVJQADd+8grDmu10Pv5nYrtMnP11PuP3G/FLCkInjyY52T+gpPjkyWfz4YfD+XDzBPhuHXufzyfl12m4JQ2iJFA/bDoAr2lf5Nn5MhbL/sATyjd4IeSfgRM0Dd6IV7PZTMSBVoxg0HcQklxXX301L7zwAunp6SiVSrxeL0laM8NrswHIe76cT+/cx8rwyxlphMquaurq6sjJycHr97KpZRMPhd3KXVsc6OSZvG+6nN/OddFmK0RrjWJ3kp8ZDWpeWS1H6VUQ4he449293LC+gwua5Hxm2cyYrzYz/T+fk1e3EUmSjmmM6PQ5+aHsByZOyyVp0VdEWbrwLfuS3/xpAUu3vU67oQ6FLRbN2JwBvy6KjBRcUgg6MYUxZeP4uORDysPLcblc/OOHf/DGhjcYkTWCV/a8wvvF77OyaSXLCj8iW+fBZm5nUdkiFhQvGJQpRj8Fzgj/M/SK7Oxs4uLiehz77W9/i0wmw+l0HhxpcwC5XI7Vah0U4R8VFUVJSQkej2dQ2gdOJj+lPv4TkZqayty5c7n77rt5+OGHCQ8PZ/To0eTl5ZGUFIj0G43GHv4X9957b4+xkyEhIcc1DTrVEASBTkUI7Z1TeWeZDJ81i7MUBbSJKf0W/gB333032dnZpKamUlZWRkREBGlnx/HqzjlYU8Yx3CjD4dXhcDgIDQ2YWklIfFn1JYam/UxcWcr3y+axYs0K9kTv4b7vTCgkgS9yn2KNcSabH9lBwZNbeM31ABEegU4xgZ81yBlrkJFrgPI9KwDI/3oe41rDaJCZsUta7FIY1vo6fDIbN3x8Me3mJrR2LS4pBLoOZvw7zK1s67oGuxRGeaxInCGJ+CunkzwpHiFpcCZVaJ99gX3K83nuwVq2+2dBfAKuex9DLybiqbqKa6eWEjdMIN8/nj1p12M2TaCxafCEv9Fo5Pbbbw9sfINZn8OFf//K3Lu/BxaLBZvNzO+fiuSN4QvB6w2+zhc2ytlU+g0AD219CIBYTWyP8mazxUD12o/INAQ2PNNbZFxaK0fyq/nPMg/Xfh/ofU2xCUgfvMvNT37F7764hj0r32ZL8bLgeXyij80tm9lbuob/KVdQ29Qze9aotDO+XUZ1jEhMeSN53ov41nM1ZjGKqLRjTy7pC2o1zJjhZcGCBaSl+Zk1y8UVtyoob76JuTvDeVx6A1E6mPmb0C6jwLCCHWU76HR2UttVy7MFzwaNLAeD9vZ24uPjAfC6nQgwKBl/nU7HZZddxrx58/jjHw+U/0YpyOgIw2PpJM0CtXW7OP+LnURu20W9pZ7X3/0dt68OlNj/YbeK7d6ZOBTgt2Sizoxm+9l3Mfy2WBrE4chtVhJamxjz9Ub+/ukPXLtpI6mfLsO88gs2N2+mtLOUlXUruTzrctRydXAWusFhwK5rwI2K0q5foLfr+O7r15iskzFJLyfEEY7GpcHitdKx6VumNwnsTBHROEMRogde6k9oKJl1OYRWzyRB1saN+ySSO2xMf/pRrv/XN5xdnkWpbxJT91VxxcK3mbTgI1o3DN1kB0EQKGkq4LzNDfx60zjS453Ej41HOToHjjJXvi9MmhZDbO1khnVqMIqx1IvDmKHczLD6YWxuWE9NVRX7a8oo7igmxBtCbGwsUkM9MlFgwegH2Rb7cwA8kpI/F6iY53yEvyxpZdy4P7PQfycZZhnbonVM0B8iA5JT8CGHtp7tWJIkBb833VUuoigitbYgNjUiSRKVX83ngkY5up1rEYAJBjm/2QNSTCxCSioTJgxMdMnlcuLiorj8chdffhnKd1tTuf6u8XRER/NF9PU8rv2Y29IvIXd2CpGp4cz9YiZ3LJlGl6RE8Ctx6VtP/CC9pLm5+WB7Ynep/yAk+5KTk/H7/cE94/Dhw5l2q4JPNffy0ZxVNLaHkzHCwLiz9hFljKXO305NTQ0jRoxgt2o34z3juUoSGdcu5+3o55lwztdMnbqE5MytRPh8PPV9NHNtnwPwivtvlItjiTN2IkoCa+zX8dd8JSF+AU17J66aClbXrWJZ+RcsKF4QXKPVaqXSUMkTO55gYc1Cxod7yN5SyKTqWkZXdSG32pn2SR4l1ioEBIRx44/6XPuC8MgT7I6/isvP342+cyY2fSNxcXFku7K57+z7aNqylo+327h4rw+NQYPZa6b4m7e48uv97PnwH7TYWsiOymZ76/YBr+WnwBnhf4YBk5OTc4TwB7Db7YMi/H/zm9/w+OOPc+uttwbHkp0uNDQ0/NcI/1tuuYWMjAwiIyODffw5OTkUFhYe0+zycC+M7r7/0wVJkjAoI1nvuJpMi4xGfyZna/YGhL/Qf4Gh1Wq54447CAkJwWAwEBERwa9+5eTuu21MuUBAbz4HlxQo9TfKjegdeswyM++VvMeSdc9xTakXR+EP5HnzuFc9i9iyOr5W3Mo2u8TTT1tYstrMx5tC6YrIpEuM4kbrt9yXr+ZL128YWZvB8rIvkCSJ7UkerDseZ0eqH5lLi00Kx9XcRFJsOXPW1LHdX0O8TY4LTQ/h3+U24rGnYvAng6ggVKtASErikksGb5yc8pypPP9lPGffPQ3dlfew55HVvPhGIm9duI4fEm9gxCPXc/PNft5/389XDTPpME6lueOgG/oO3Y6goOkPRqOR1NRUXn75ZST30YV/X+fVH8qUKVN47733mDdvHqJYRdQvL6DhhidhzDhKfeORm1NpMlRS3VVNdVc1BW0FxGgOfs/2tO/hmcW3cs86O2QNo/yWl1FYkji7Lpa5tiUMMwcu/y5JzZwqBbcVKkkz+pn/n3oeeLOItV/9K9gzuWnFK3yy9EG2te8mqzMEk02PJEk4fU4aLY20h0kk2gWaIkSm7tWzXxqHXkxCQkCmHrgQBhAEmDvXjiAIPP20hZAQmPqbOZjU6WyyX83EG3N4b8YBkZeTy4UNcmZtrKG64gNe3vkCt/vOYlS1GVPlvkFZDxBsVWqwNPCYd3ng4ACFf1hYGFarldDQUObPn8/MmTMB0GaFkt6azGXVCgQEPvxahUISuGNNJx/nv078nlLinAIN0bGYxGj+6fgnsYYktLocUlK3UGpL5uIrLsMhE7GoJCIPVEkYomJwDhvOlFYZu3Z+wdavX+TT756mYPsSznrsTdLqjLTYWshv3cFL793M8vfvwypFYLWMRu/swKnqZKxBxmXVcrJqc1G7NXR5reys2ci0Fhk2pYTGGTooGX9CQ1EATimcmBQ1Hr+W5RsUCH4/SXYZyz238mzsoxSljkaMTyCty0/rrvUDf9zDcDqdwQD1tmXzmLGqhGYxg7ThcjKun47q9lsHPKHm/MtHUu8fQb7vfBa551LvH87oiO3oPDk0GGu4ZPUekrdtpmbXai7b24aztRqaGlnivpUSQc3GCz5A9873XCf/AbsUhlmtJTLlHvbvz6RRyCLSI7A/VmRsh4y68y5E+PwbFqa/RIFvBpKup0he07CGj/d/DASM/bwRXiS/G9XXy9B+uBR9WxXV0T5S6nPRHe7inpEFwL33WhkMpk/34HYL3HabnZgYDSUJUXyecBcXzHSzreImbrghUCExbLSarFwtk9PzaDZPxWAcvAkfhwp/r8uOXJQPSo8/wN///vdgO+RFF13ElroiJj97NdNuz0Wtfp/9+z/n93+7jFABmlVeFja8zeLOxYRL4UTWWdF++RmrvVdy0Y0ROJ2dJCYquf76Kxkp309F7V14FaFYhGhasmZTeNXzONQavhd+xVeeG7ih7KAvRdqeWtYsf45H7v0SeWsbDZYGCgoKeOWVV3jxtbv5664Q0tsEKkP1JNsErqpQMKEmhULfWfyizMt1ZQpQKmDY8AG/JkJSEubwTG5/ahIGMYG7lrfxgOI8LPP+jfea63juqwpCGhq4ctlW4u1aft6Vw1+/dzNRJ+M741bSihvIbXTRbGse8Fp+CgxODd4Z/qu55JJLjtraIJfLj2gB6A9qtZrXX3/9/9k7z8Aoyq4NX7MlW5JNr6RCQkJIQkil9yJNQVSkWFBQsAGC8ioqvIqCvvrZe0ERe0EUURSVjnRIqCEQkpDeNmVLts73Y2EB6ZAAwb1+ZSczs2fqPuc559yHkJAQ1q1bd8n7u5wUFRU5o93/RlQqFR06dEAikSAIwjkHQ8ccf09PT+fkwdWK1WpFKpGgEwSOmOKxiRKKPJPpf7sfhpfcLynifyIeHh54enri7S3i7W0lzN+Hd18egKrxb5YX/kyJpQJjrpEyWREvRD7IzIJHuK9awE9vYXBuIWGf/odGUUFu25sJDPkOiSST6upiLBYFcSl2pq15jTFpW8jan8Yqy0AUmGhzZAcv/vUUAQaBfSW3ouj1BP5Z7lQo61Hu3UasZyPX5bgzbFwdN660USmqnDX+RxqO0ICeaFMt2voYInU21Mk+CILA+PGGJjknxzimhGz3C+TndQJz5tRjsynZsSMRwdtCcnJ7FIqt3HJ9LMv+40+B7ng0/Iv9X+AmcSMtKO2ivvtY9xZBEDCZDMis8lPqPCdMuPgWgv3796d///5YrVZefvllHnpoJi+8MJnMO3uy5F0/Bu+fS0j5dhbuXchLPV/i0TWP8khpW1a7V/OB9QNUUhuzFxZhNPjDf5/j3bfSyTTvpJXkCCpvK7uERMqHzeT9dZFMLZ1NrHQf31v6chNfAQKdd1SzasHTpN78MJvWfsrrvxlYFmNnpv4twk13UJuTwzs7X8RYXYZnQz0SZAzMkxFfJWFJaGuUFjOUFkNG5kWfgzNx7DUiSCTEjU5m9bouvP5YAN9+78H6Hn+hjAzC8ukiMjb9jxcr9Pxc9TsBmxbj1daKdksFAW81TRT4WMbN3rw9lFm1WGXuTeL4H1PcP7FMrPuodLQz4+lndqQsBxgdJ0FuF5j14SHse0WWBk1jc+Yk6g5amJu4hvzP+9NoC0PdYy8dW/9IdPQNRLXO4pDVk1ZFfjzg8zxHPL3oGdsKxdKFAE0X9AAAIABJREFU6KNfQ3nExvg9MnSeKmSlJsIK1nFErmGLfj/PvX+Y57uYabC3JkgvUi7q8JWKGKw+aIR63CxyPE0Squ0W6mv2UlV0F7GtP6G0UYXg0wSdjjw8UKOjVvSh08Qu7JufSIbcIUxpGXUH5uJhJIYt4Zntc/hunp2QyWPYWd/0g/01a9bw9ddf06ljR2pys/BpFCjueSdp/4mmvtiGTnfpSuae7SPRix7ssqZQP3wiq7L/IrNrLvlfRHPX0uW01Ur4XGYlb/1y+pRK2TP/QdwtJg4q2jFykg9arcDTC5KZ+9hG7n98IVPvLibqfiMymcj9uz0wlirol29ivX4oi6ruocMP6XRsvRbZXgX6skJO/PXdtH0xKr0FEsZTXlnOF3VfECrKGFonwd8gkLP2Owwy+Lt0OpkZk5AaNRhFCQJ2ZK0jAIiObprfQ4Dbbjv+O9KunRWTycLo0TZefjkfP7+uJ59H/2osByKorD1CRBN9f1FRkTNoYTDpkFvcmqTGHxxCfcfw8/OjtraW665ziNl9991BnnzySQCC/Ix45QXz7JoclJkBFB06RHD1BgSbjW3ho5l9bzTLZ9no2bMnsbGxVNyWxucf38Lzr9rZIVlLqz0+HBEk/DJlBlu2jCZ593K0FT4skM/gPuEl+i/NIdldxNYo49YPN/KsSsfWndt57u5nWTF/EQE/FPCMm8iIW4zIRDVhDQJvGW+jJOl6wg7cwuC8KrJ8QhCkl97lBOD22/Wo24ZBTFuUJRZaPfUkzrejuzvo9UjtdmIL8ogqKcZd78k03ftUSG5k+vt/4CffStn/bmoSW1o654z4v/3220ycOJEZM2Y4l+l0OubOncuUKVOYO3cuuqNKyaIosmDBAh566CEeeeQR8vLyzrTbaxaz2YzsEkRdWiJRUVEEBQWdsjwoKKhJIv7gGAC1tB7vtbW1KJXK04r7/Zt4+GFH6zAvLy+ioqLOuq6Pjw81NTWMGzcOq7XpUnKbg5KSEiICA9HJpaRK9pP9/m4qRz9K8IO3YA8IQvZY09Syh4eHO+sJAdS+aixeAUhFYH8BTy3TUvvnTwRU55Jw5zS+W2hhtuFlRm/3YcLaerDZWBd0O30nRRIXF8e+fftIStpM27ZrsCQWoEvS0PEmHYtME2gXcZCDtjhuXlnJqMpgRu70IxAtpWo5nnWOVF2TIY+YSgWPVH5LarGKMLEaOxKoreX3gt+Zs/4p6mVWfI0CbbO7oM27mV5jA5rkXJyJ4cONTJvWgCA4NLUyMhxppR4eHkREbKbjdX64WdRIa2r5ft3bAMjLK9mbc6pi+fmi1WqdmU5Gsx6ZRe7IR29ijv2eqFQwapSBhQt3MfOhbPLtbRiyw0hh6T7qRk1EVVhCwtvfkvTtKhav/oyxb65BpWvkUel7DHsqkqA2O8iXtyXblkqt+xzmRv+BIa0P734u8Kd4HZ/ZJlHWdQx/+90C4+6gd76UdTu+4esPXkNTWYfWGsSIAzIO2OKpFX1Z+Od8un66isRVeynycAzqx2fLkdoFlJ07I79hGNYxdyGEhTf5OTmRITOiufelcASplFGjjGTVt6OkVoNx7H3M6bGbUjGamzY5xiheJqitb5pysWPCmQAHvnmdhxaXovNoQLhEx1+j0Zy2k03ydf5kyRziuqZWR6NomqPvhX172GnLpDGtF8/Ok/H61ypSR4aSb2sLEgmmoCDc3PajVCpJ66IheUcmRUdu5InZUp591sQDs5Q02rzZ62uhe6GUYL2EmFKHDWENAoW71mDfsokd1jQMVh90aMiw7menn5JWOoG59hdZY3FotQSZGylXKGi0NLLENI7kPfH4VQY1ScRfkLuhuftWZMMGkzg4hD1tb3X8Y+gNrMp8ln4TWpGeHobRWEeZIhpPg4xqYzWF9YUsPriYYl0xVcaqM2pYnC+VlZXMnj2bW/28kTSa2BcxnCx1X/yivcjMNNOly6V3IhI8PMjv3JXC/iNxD/bgiHsgEX3bUeYVQ4dKKSqrQFKF4/6LqpXwpzyfaK0ERWQUffv2ZfhwI/ffryN5TBxDn0kh9clB+Pvb8fYWSc20sULozvyVbmS59yWl86/85z8NDLzOjKbei5LaAkw2xzFsLtpA8md/wOqViIUFrCxfybSkaeQp8ompkdCuSsKXWz9G5yaSXTeYHD87Rxoy+NY0jr/iH6P3mCbI9DgLU6fGMn26gJeXko4dfzzl/zqVO2q9hgrDqW2nLxatVut00A1mHTKzvMki/v/kWNnXL7/8wqBBg5zLQ0NtRB9MQGkT4O/1hFWUIbPZ0CV2w/c6x6TE1KlTSUhIAKDrE3dw52P+pPX3YPFvgcTGObK5ZB79UXrnIm9dxlZrZ34ThrFn8Gy8zALSqhim6j9Evf8gN+yRcaPiRpZs/ZiAWoeeicYs8Pxfjt88UYR67zbMWtiKDxofpMgWTitN02Vv3nmnY7IneEgqhyVHxdOH3kD9U6/z1qjdLB70NaIIg9evJv7wQb6x3ImnUMuzf6oJNEiQ1tVj37m1yexpyZzTI+nduzezZp3cgmPJkiUkJSXx+uuvk5SUxJIljlrAHTt2UFZWxuuvv869997Lhx9+2DxWX8VUVFT8qyO8JxIcHNxkjn9L5KuvvmLMmDFX2owrTqdOnQBo164dKSkpZ13X19eX3bt34+vry9atV/dLuqCggMigIPRSCb2UW/luqR91dQISCXi39kHWuWkinT179jwlc8Y92IN7N/ryyMKV+Gz6m+i/c5DWOFS5FRYJebYYdpi6YxTdKf/P22wfMJf0PkqGDBnCO++8Q1KSL0qlDqu1nsmTS1hx5AClKf24/dux6JVKpLV1RLz8AYft0fSU/4l/lT+edY6Bzl5/O5WlA3ETTNz/S0cCJOVI7FLq6srZsHohnb5Yx24fBRG2egRRSr3og0+fjk1yLs5EfLwVb+8zC+kJCgUSjTsTtys4uPB/lD81hdhfNlH2xTsX/Z3HIv4AjRYDcou8Seo8T4dKpcJgMNC+vRWpdBF1nmCRKAk8VMqr75aSVFzIOx9UoLYK9D9kZ8kXJbB9K1VKb6IGhPHKKwoio/Zi7TcA06CbefXrt/joowZGjDDi3yqY/Hh/5OPG8ODH8Ry6+xXmm+fxpvFpJJZGNjf8TP+scJ43PI1NlNBGmotFG0O739bS84iU4Qdk9M6XIqpU2AWBgr6TaZ3iRWx7qDR4nvvgLhG1WiQp6Xj98IMP6hg+vJF+/UzMeVXGopSPWa4cQvV/XsO7UaDWcua2lxdCTk4OcXFxiKKI6eB+UsukdNze6ZLF/dzd3U87hlAoJVj7DOLzhFuYovmVBm8fhBdfgbaOQfAKcRDXP9YGQXDoykni21EfmoBHagwpmZkOEUogtos3Ndp0dNIgQnun0LFjR9x9FXioa7lxRyCWom5U2I+KsUZFE6gX2Fe6E7/yBn4wjUaR3wWbIYhO8g1sD7HS/mAEPjFm1oROQOetwt9LwpooMx0KfUiQ76a0uifeZpqmxh/QJEbStosvgYF2KtNugLvuQZgxk61b5aSnm+nYsSM9euxl3jutmaz/EtHcyOI9XxKrjOCvvN/55sA3J3VCuBiqqqoIDQ1FnbUNm13Bt57TeOmlWgQBVCoRX9+m6SQQmdyRvYWFxMeb0WoDCQoKpCbkeBZIhwoJo/fICK8XWBllQ1PVitAYhyMmk0HHjo7nYvQdNiSS44GTgQPV/GnthmiXIQ0+YVI2JARNgxclhlIe+OsBvsv9jqWbFjAsV4oAfP3C8xyuz6H3T5t4eUsQMVoBH5PA//0OQ7JC8ERHmVqKTR9CQeZtZHWcTMfUpmnnecZzFBlKdLQjln8sRf5E9Go1ar2GSlN1k37vsUCU0WJwRPyb6d2fmZnJli1byMrKIj093bk8zN9AiT0UqyhFeOppfuw/mDdH3UbO9M9on+Z4BwUFBTntlEjg3nv1qNUihw/LSEsz4+Ymsn17O6zWr9GGV/N++wXEddlGVvjNyBIS+VF6J5K2UmrsfnR++ztu02qZsl5kZI4MevUBIKNUSr1EwleTfiB9Vl80ngKh16fylmkmQx+LbfLzceskNz7rtRhh0dfoZv0f87fdypg7bJjbp7FF5pjwqNd4Udj7DnrG7MVe0ZEaux+iCOzKPqUTzr+Rczr+7du3P8V527JlC7169QIc6sNbtmwBHP3re/bsiSAIxMbGotfrm7WVztVIaWkpISFNI17V0unTp8+/dhKkpqYGnU73rz3+09G9e3fatDl7vZefnx9Lly5l5syZrF9/aYOz5qagoIDwwAAMcoEQmYGJE3UMGeKoYQ8MtNFEGW6MHj36lGyX1DQrO6yOQcB2awZtDiQycr8jMpxtS+H6tK3sDBrOV+1e4cO8EQ5HQAJqtRo3Nze6deuGl5cX9fX1tG3blj///JN3PqjHP1CC15BBmEQ5GI0c9utKWlcd6WuG4WmWoDKqyfW1c9DYmxt9fmSTuTeBQhlKo4qPa35j3AebGHQQNoVaCY8QCRzemczpnS85CnopaDQasrOzaRXrRpE9gvC8WF7X/khyuQTRakE8psZ+gdTW1uLt7XBmDNajqf6K5on6dOjQgV27HMKESqWSsqoqONqWy6usErsgoLI6PD6pKCC3CzR6aMif+wc9hoYQF+fJbbeNI6l3CKbASMLCwvDyOu6cdBmcz3WjShAEuOMOA336/4GvbynReW2Yuq6GPH1nqmRBFNkjiFavJyhrKAMPy7CKUgxWH4bnylgU8DB/zlrAd6FPkZpqITHRgq9v8w76z4VCAbM/DmFx8kB+0I3ky9qH0doMTTL427x5syPd96gQmkWUEVISccmp/hqN5rhw2D//Fx/Gt4Y7CU1Ucpt3G/4WpAjf/0TZh4vISe6G2lftXFeQyXAf0oeYCb1ITU11agV4dE9B7xsJCYkIJ2Qn+vqV45+XygrzDfxpHkyJJJQ54kcIMjd2BdpJLpXj5m7DraATCTs6Ey3JpV1OPKur7ya8Ry7yvr0oTA7B28uKaJNjOTSIMf3z2GPrgJdQi6C+9LI/gNatbaSmOp5ZUalGePhRKuzBBATYEQRHwOGxx+7jzTdrae+RhVmU0/jpB7QfPJZx97/DfYeD8Vi7EfESVN5tNhtyuZzahkpyG7pwz5hS5PJzb3eheHgI9OwZxurVz6FQ6AgMDKRU7U1WXALfXvclPxjvJKlCSp4pCasESqp7kNH33FlHcXHhFHmHsd+nN+2uO+FeCwrCo8GLLYpKuucLUFXFtAOBSBCQ2qFw1yaiC8uQfv4pibvzKbJEs92agcomYKtuT6ZsAzqpDKXBg9QOBjQakcuZqPn446dm2UmDg1EZ3Kmy1lFjdESgdWYdOrPuor/nxN9jg/Wo499MEf/U1FR++OEHwsNPzpwKGT+IA2I4T3ZYx7M5k9isvIlqq429e+W0b392IcX77tMRFmYjKclC69Z2pk17EG9vFd6+MiIit7Bh0wF2zniGqkEjiB1Wzk+tHeUFms8/JeiXVdTqYnmo/HU2W7oAsMJ8A0WGdvQf7nif3Pp8O9zG3kJA31MnYi4VpRK6DPPgu9yufPKJO9OnN+Dvb2fErSIvRk3ntyee5vu73kARUY2h/nd2WDOZoX+Hwz6dHOK4Jae2Lf23cVE56XV1dc40Fx8fH+rrHTPoNTU1Jym/+/n5UVNTc1LNyjH++OMP/vjD0S/6+eefP0Ux/mpHJpOd1madTkdiYmKLO57moHfv3k2+T3d3d3x9fZslff5M1/RiePPNN5k5c+YZRe1cnB5fX1/q6uro0aMHv/32G56enrhd4kC6Ka/riTQ0NBAbEUGjRIqnSkqnTsffc5GRUvz8ZDTXa6DPo334v/UiSkkuS72eJyLreyaU5TBD9QYWjS/PvxHLh9/GUm+H1+Ydc3IcA8KPPvrI2XVj9erVpKamUldXR2ysY1Kmy8gA9gR/itfKJ6jq9xidLfNYvq4rnRVrUes9KFPKSAp0IypeyqLlgxjk9hNKYyL7bSVMrVWSZU0hsqicqKBGbvy4MxIJzTL4O9/reu+997Js2TIq0r35Ke53ViwspGFgVzxWPIEp7DU8qypQdLjwjASlUukscdotWpBb5PiEhCBrhovet29fFi5cSM+ePUlMTKShoQHNiLGU71mEZt8ucsZPpo2+jo3icDq9fyvekloCXnyFnMMx3HmnHV9fR8XuyJGQliacct7uv38CCxcuZMcOGQ8++CBr165lwHU+7P58AInKBaywtUeWaKP49qUcfutZIgscE5rvdvkdy8o/mKacz9bKtqQZh3D7HW4kJamw2yEggAt+9prjeb35ZglpaYV896GREjc1fm5uSC5Rdb2hoYHExERqV/xMo8WL/xlnocKI2mbD/RLsz8jIoG3btqc9BwMGCGzZ4o+X1+8MHfoGb7yRTWiolaffq2b0Xd3x9z+5RexttwmEhCgICtIwffp0x0J/fxoGRpOZKeLvf3xipm2aip0/xiOVW6m87Vn+DniCbkYDX3w+liD9e9SW9MGtQxnCVg9kNhnBbiVErH4BuaSCRo3AqH56li+34l+pY+JPvcm1JTDhlZt5NXE3vq29kcvlTXJd+/Q5/ndamoSqKgXLl0uYMMGOv//JUdeoVjpWKTxJra8BJFBXi/jUY0gyzbit+BWvmU9clA1qtRp/f39yrfWgb0/71EDkzfDcX3+9gL9/AmFh86mqsuLnJyWyzRd8UDeV1kFDKPRvoIYEDpb6MDxnPHm29twzKgmZ5tyZlrfN6MM3O27lqck2Cj9a6hyrBJlFFrS388uHKwkwrkHi5UWONR5tjRzvlAKuzz56LoFVloH8FjyU94L+R35WGzLlGyjQeaDSuzNurBtCohK5vHkc4vMlNrkjdfJcShQio5bdxPZJWazctxKr3cqYxAvPyBRFEZVK5byXTaIZucUN7+CQZrkHwNEifMKECc6JZgCGDuTvtjFMHh3D3XfbmTIlkvr6Aeh0GhIS1Gf9zb3zTgAPRo1yfBaEBJ577jlsNnjuOSX19fW88KqFlJRfmT59FPNrlZC8ETdjLeYVv/GLeDPvf+nN84++S6cNXflBOpif5nqhPGHy4513AJrnfIwdC0uXCkilAgkJx7/TyzeUhK5B5C4JZPv2RxG7x3Fk42gSurZi34GByOxrUVaUoElJBRwTQB5u/76s5CYtRj/Wb/1EzlSXfUy46BhVVVVNaUqz4+/vf1qbc3JySE9Pb3HH01JQqVQcOHCgWRy5M13TC8VisWAymbDb7a774CIYP3481dXV3HTTTTzyyCM8+eSTlzTR01TX9Z/o9XrqysuxIkcht530HRqNB/X1RqqqmimtTCNDP/AmqpMCaXW4DdoDERy2xiDEaDiozcO9VTp+fg3Exlqpqjp9RDs6Ohpvb2+0Wi19+vRx2p+eDguye5IdOYegBjPbFCZKJJE0hm7AXy8hvy6OzJRKCnu0Z8/y9hzo1xGv7RoG7ZOxkwz+a5hPt1/+IjDyM7Ta5rv/z/e6SqVShg0bxrzst9m4fSQTkz5BWNqBTxv7kar9gay/l9Gm1ekjrGfDYDA4v7/BpEdukaM1GhGa6Zk/cuQIW7ZsoX379uzevRsPjzJe8R6GvOe3WA+UUVWlJyxMS3byW/RrW8HbC4YTHGzCbq/jmEmCAFFRcDoTb7vtNl544QV2795NUFAQKf368vuiNQAcDghFEVTKDxt6Mumle/ntWS0Taz6hby8p+zZ6ctgWg0m5h7vuctSgH9u/u/vpv+tsNMfz2qVLFxYtWkSozM5mNyXVh/MQbJfWbcVoNFJVVcWO7ctRVkaTZUsgRboVg1qN8RLsPzbxcbpz0LYt3H9/If/97//QaDYwfryGmTPz6du3J4MGWU7Z5ljiwD935e6uIS7OSFXVcR2ViOu78ePiWgR/KxaFjJxKT6ZPNzDhzTieWenDO/YbSLu+nuKtFkQEcvr2ZdtPnfnk5UMsOrgBszmbmJhGNO9uxmbpj4hArUpJ4C090fTPwGq1Nvl17dhRwvvvu6NWi0ilulOOs12CjJ91fvQ4UkfRDQ9TvqOUtCNf4W5UUZS/F8tF2nPs2a80VKExKqi1i83y3B8L8lZXO57dmhrw9s5i69ZxjB6tRSarZG9OGFH2Wh7eqOT/PL2pNTWC6dzdU4YOhXfesaNQVKHRaNi9ezd2u51QRS3ti3wJMhgAEWprWWGZgL6qiu1pm7i//LijVWUPoPfoLXyg/wpJspHBh55nWYMvKqM7dXI5Qt2VH/9oNBp8VLVscnfjxg317Gr1GdmqXMw2MwOCB1zw/vLz8/Hz8zv+7jfrkFvk1DY2Ntu7/4033jjt8+PrG8WAAZVUVYn071/MW2/F4O9voLr64jsoFBYWEhAgxWSSoNfvwmodychxRhasfJmJE/WwZQu6zxOxyIz4JPmz755dRHxagk6nc+q9XQ66OJINTnrmb789jMOHpWi1diSSEvzb9kMTEcm991p5a2wiEQ0C+7PW0DqtMwDTVk3j5V4vIxGuDR2uE8Vgz8ZFHa2Xl5czhV+r1TqFp058GMBRA3m6aP+1jE6nu+rVyFsywcHBlJWdLM60a9cuGhubrk3YpZKTk0N8fPyVNqPFMmnSJAAiIiLIyMhg586ma7/V5JgasSJFoTr5Vdq7d+NJ0bTmIDPTzNatPRk9xoZw3WD+vuF1pszvQrduBxAEgdtvN9Cp05nT2N3c3JxlSfPmzXMul8th0iQ9bdt2YPPmSg7WN+DWOZ0DGeHE1psx5o6gQ09PSqurCIoqhYQogsvC6FsgY7n/fcyfeZjfLTegemhysx7/hSCRSFAojHzxRTV9xvjwW/Eshrj9iKU6nvyC7Ze8/wabHZVVbLZ0T3Bkw2zYsIGYmBgAbLbd7No1mscfr+eJJyxkZHyHh8cSLO1786N9DK+9VnvBImNKpZK1a9eSkZGBEB6BMHAQtg8+wxAfh92+jQ0bFHRICWfcGx1p038rNtsK3EcOY92tC3n0wwnNcdhNgpeXFzqdDn9vK0aUzg4UF0tDQ4OzBHJV1UYU+V1I7ixHmz4IbrixCSw+PYIA8fHReHt78eWXWgYPVvD1122ZNOnColYPPqgjNvZk8dTAXn1YpkwhdGwMyclm/PxsqNVqeg09yJyKL0nvo2PEjTdAejDayHiWtYrgtd9DCBrhUFHfu3cvcXFxeI8ayGZrV+KGRAGQ1FHEL7iJ6p7+QUCAnZISKffee/ruGXEpnrT7eygx1QLv197Db51ewnTfo/xQPYVK/aWLPJbZTHgZpeDZ/FoWxzhw4AD3359Njx5m4uM1GAzvEB9rZZu1E5pg9bl3cBSlEj76yJH63rp1a/Lz88nPzyeSAsYs68N8w9M0vLiAvAemkZPSB+8af9wtoLAJ5ExfBH7+mCMiuGXUdSiVArUmD4LCJHRfdR0SuwxO0+L5ShAWFoaHuoaHfuxEx721HPrgOUy5+xDzDl3U/rZv305amqMTzEvbXiJHacDNImu2Gn/gjILh77+vRaVyBFyTk5OZMMELq/XS0uvatWvH7NmteOONNgwbNgxwdGTw9bXz4osanv65H52vd2Qe9O/fyJNPenH33efncDY3vXtbWb1agVKp4MUXXyQqKoq+fXegUoHdy5fQBglHSvY4199dvZtqY9NqP7QELsrxT09PZ/Vqhxry6tWrnW0t0tPTWbNmDaIocuDAAdRq9b/O8T/W99hF8xASEuIUKQL45JNP2Lp1K6+88soVtMoxS3qsr292dvZpRWZcXDjJycns3bv3SptxCqIoOjKcjEasohyl+uRsp/btrbi7N43A05no08fE7Nn1+Pra8Yz2J0eWSlSUwFNPPXXB+zrdwGLaNHe6dPmdO+64g4gIG+4e9bRWyAnPj8OjZ082bNjAxIn7uO5Wh7J2g6hBHRdBwgO9eGi+F4y4+lrneHqKeI65nrq4royaF4e1IZKK8osbAJ5Ivc2Oh1Vsthp/gFtuuYUFCxYQGemIVDc2buLVV3V4eIh4enqi0+mw2WzcfLOJYcMa0WhErr/+wiZEMzIy+Pzzz2nXrh0AgZkRzP2lPzfd5EtwsImoKCuCAKGhdpRKM+Xl5fQaqOHHne1o27Z5nLumQqVS4e1lxYgaai/N8d+1axftE9tjs9sw1lZiNgUy6BY5tf7tTqqbbw40Gg3PPvssl1Ltdqbaa/+wAm68NZr+/U3OVpSTX3uMJ35OYuy7t+Lu7k6v6f0pDBFQqdXExh4f7+Tn59OmTRvUjzzEavVN9JzTHYBRo4wkJDRfh5a33qo947tWER6E3ODDj+ZRjLhLhbunhCXGkSh13pTrL03lXbTbKUEkqNF6vLvCZcBms9GlSyqC4BgPyeVyUkeGs8D0AOmDL2y8HRnpyEiLjo7m0KFDFBQU4HnPEHbI++J24/W8vmUIDZ2mUCcvRWlS8dh6N0rc2vLMb4P587FN+N0yhPj4eEaNMlBTI8En3AOtJRSZSopwiSKXTYWPjw/BlsOU20NpoxXIM5XAH7/BH79ha7hwoc+8vDzatGmDKIoYCg6yOFSLxmJr1knfM6E+Ydzh7u5O374qHn/80sRLx48fT2ioF61bhzknOABGjjTy6KMNPP10Pf36OSaUIyJs+Pvbadv26ujAJAjQrp2FgACRqKgoIiMjyc/Pd/zTx5corcCPtmwK6gsw28zIJXLKDE3T5aUlcc6fjldffZUnn3ySkpISJk+ezF9//cWIESPIzs5mypQpZGdnM2LECABSUlIIDAxkypQpvPfee0ycOLHZD+Bq4nSlDi6alsTERDZt2kRRkaM3b3l5OXfddRddunTh559/vmJ2fffdd7z66qsAFBcXExoaesVsuZYICQmhtLT0pGWHDx++QtYcp7a21jGpaTJhRYZSfWVTxZKSLBgMTW/DE0+MJi4ujvvv16FQNJI1NJ7Bz8UjDQhkz549DBoUC55eyAUu+PNkAAAgAElEQVQzf5oH0ecOR837iHHSq679pkQiwWazIUgkLPhRgkePNNQ6DyrrLr3Pd70o4m61N2vUx9fXl9mzZyM/qiJmtxuJizvuZBYVFREWFka7dtazZnqcjdTUVPz9/ZEeVaa8804Dc+bUM3SohqeeepK5c+uc60qlUqxWK6mpFkJCbJdVxOtiiImJwU3ZgFFUQV3duTc4C9nZ2fxq/5Wpv0+m+25HWm3CgMCTugs0J+cSSb1Yfv65C4GBnkgkJ2sUJiQcL1nKyJDw7rsZTJkyxbns2LMuCAISDw+S08Hf3zEeai6Nj/OiZ2+qo+NYk34/6ekW+vc38e3KKDoYS6k0XVyrscbGRofuTEMD5UoZQaKkyXqVnw/jxo1zigaHh4fTt29fwq7vyK7gYSTfk3pR+wwODqa8vJzS0lLa3HMzPyonMmGWJyNHGti3z424+Gzkgpn4chULZI/w0QItH33iTXKy5ej2dl5+uRZJYADl9mCCvI1NdryXiiAIJN45kDJ7CAfq+lChFsEuEqmFwqyVF7w/u93uKD1c+SfKX5Yz648A/PUyUDbfu/9CuIy3IgDvvae9qt79N99sZNw4x6RlZGSkM1AYluCBpaE1T/xpZ+HeheQW7aDbXj1lG3+7kuZeEc45NT1t2rTTLp89e/YpywRB+Nc5+ydSWFjojMa4aB6kUimzZs3i5ZdfZtKkSU5Bmt69e/PMM8/Qr18/VCoVq1atcooL6nQ6ioqKnFGs5sBms9G9e3e+/vpr4MzaFi4ujH+eR1EUmTRpEl9++aWzh/qVoKCgwPGsNzY6HH/VlXX8U1IsuLufPt21KQgPd7SDMkgrGDLW0eorPj6egABHKyifu29mfa4XIzpfvVHfsLAwiouLiYiIQKEAMSgIuaDEZG1E1OkQLqD1qN1ud96bos2GTgAPm51mkfY+gWOpl3DqRLPJZHJ227lYlEolb731lvPziVFlNzc3YmKOO4AhISHU19ejUom8+uqlRdAvB3FxcZiFxRhF9SWn+jfW1OC/7xAzlxThVSKyKao1Uk8PJk9uvmfwcnA+QqoSiSNj4ESsVutJ3Z9eeOHquB8EiQRF576YGxYCN5OYaOGZ56ysG22hQLQhWq0XnKFRXV3t0Biqr0MvUeCnvrwBnwEDjtel+/r6Mm7cOADmzKm/6KCz810mikilEqZPb8DX146vr52EBCurV3cg9/cdbKrsRkjPGNRqkRkz6k/K5FAqQQwLp9zuQVDwwYs/wGZAc/etrFlczKLcyXRVxRFfI5JYKWV3zkpadx9+3vsxGo1OATvdhr9wt0Cbcm/KbRZHC5F/IVfbUFciOX4p1Gq1MxO39xApS18fxT3aFwlcvJx1qjX02lxM/q63YNgjV9Diy8+1oWhwlZCVleVK8b4MKBQKFAoF69atO6mv6fjx452O9xNPPIH5aJuu9evX8+OPP/LJJ580q109evSgrq7ujPVYLi4OQRCcJTQHDx5k0KBBLF++HHA44K+99tplt+lEx98uSpGrr+w1V6tFZ8/m5sLT0/Mk1d45c+Y4//ZKaIXg53tJ6cfNTevWrcnLy3N+FgQBb08LRlEJFReW9ltfX+/UtsHUiE4mQyNcvgm/f14LgIcffviUlk8Xg+I8B7ApKSn07dsXuOQOdpeFqKgo6qx6bEihvg676Hin2Ow2vs/9/oL21aaoELZtxaekhlq7Pz79Ly7Seq3g6elJcnKy83Nw8NVT8jhrlp7AwNyjk3WQmCwSpjZRI1FD9YWLsVVWVh51/OsxiQq8vK6OYx00qOl0jsaONZz0uWfPnqTNu5vXIxdy/QxHcCsjw3JSqjkA6RlIY2MIvm9kk9nSFEgUblTRjrsiPqVM7kFdVQal5X3JLd9z7o1PIC8vz6mxkm+rJKhWjRE1KowIV/OP378YURTJzs4mKMhCVbs+mBUarltfwUKP/aSXSqhs5pLMqxHXndqEHDx4kLZt215pM/4V9OrVi/fee4/ExETnsoiICMrLyykvLyc6OpqsrCzAIbY3ZcqUZlXYPzbgnzhxolOczkXTEBkZSXZ2Njk5Ofzxxx+MHz/emb61cuVK3N3dWbFixWW1qbCw0OFkHVVPFlRXtmXR5SAqKuqkFp3HBkAAfn52evS4MCG5y80/HX+A6KBatHY/qKy4oH2tWrWK1NSjzp6xEb1cgkZy+bIdQkJCTslgio2NvWzfD44I+on3wNWOTCbDIHdDAHY1HGTeZoeg5XObn2NV0SrMtvMrjzCbzbhbjq+7rvc8kvv/u9u2Dhky5KRJ+KsJpdKhFbNr1y7nsqAACzpRc8HPPTg6UPn7+0NdHY0o0Xide5uWgFQqPaNGlSAItEv3QuWvPuukjiAIBCYFEtwxqLnMvGgWLaojyGcfyppwaqs6sdeShqXywuq7i4qKnJOrh7WH+Kn0Cart/qgEwzm2dHGlCA0NZfHixezevZvhs9uxoOdPRNZLGHJQxoe6GVgFh17HvwmX43+JWCzHW+hYrVZXtPcykZqaSmpqqrPe9UR2797NhAkT2Lp1K+BIgVU1Y+3tiSm3EokEtfr8lXVdnJvMzExWrFjBxo0bKSwsxNfXl6CgIIqKiigrK2PixInOa325qK2tddxTjUdrGa+AsM/lZsCAAaSkpJz2f926mbnhhquns8bp8Pf3x2w2M3/+fABKS0sJbWWhQfS8oIi/wWBgz549TuGj3RVZ6KUSNNLLl/M4cOBAZ7TdxfnTeDSbYXXZBkr37mTlkZWkWYPo8vs+yld8d177yM/PJ9jdHYC9w5/mSLvryci4OE2Fa4XIyMhTMlCuJpKTk9m9e7fzc2CwHT3uUFkJgNlmJqcm57z2VVVV5Shxqq/DJCrw9Lk2htGRkZFnbZOsUom8+672nPvp1asRX9+rz5EKDlYi9asl9u/huNcG0ijxAF0D9qP3wPlw5MgRwo72yMxvLKWhuiObrN1QClf3b9+/mbFjxzJt2jT+/vtvQkMr0cQ38rHlfmZtcOMPy2AaRZWjT+a/iGvjjXUFycrK4sMPP8RsNruc/suIIAjMnTv3lOVBQUGsWrWKzMxMGhpO7mUqk8mc6f9NiVar/dd1r7icREZG8uijj3LnnXc6nbbRo0fz8ccfO5+5kJAQiouLAcczWXOOF/mlCHH+/PPPdOrUyfGh8WiUuxnV3FsCgnD11fr9E0EQmDx5MqGhoRQUFPDoo4+i8mo46viff+Tvhx9+YOzYsQDYRTv/3f1/7IzSolJevpRBhULh+r25CHxbt8HNpKDcVMHUj3fy+u9Pct19LxG0K4/Snxad1z5yc3PxV7qhEzV8f6ArDzxw+XpXu7g4WrVqRUlJifNzYLgMrUzBIwVvUm4oZ1/NPt7MevOc+9Hr9ezcuZOgoCCor8csKvH0uzaG0ampqWRmZp51nX9qO5yO4cMbr9rfghoPFXarGotcBkFBhDYIlGStOmkdo9VIvfn0yvjlteW8feBt/rf2acoljXRkLxul/VH1Ovt5c3Fl8fb2pq6ujm+++Ybi6m+pDk5GFKFe9HJk/pSVnHsn1xDXxhvrCpKbm0tJSYmrvv8qIT09nR07dqBSqVCpVBQXFztrVlu3bt3kivCiKFJSUkKrVldHH9N/C2q1mvDwcKcDfmLd/5IlS/jyyy/PuO2WLVvO+v9zkZ2dzcCBAwEQj0b8has42uXiZIYPH868efPo2LEjWns9otmD2spC3s1+97y2P3LkCK1btwYgV5vLuMBB9NwZ82+f+2kRdL7uOpSNahQ2gRithA/fqUCCQLBOQrn17NHM4uJili1bxqFDh5DKbezXdePREVuual0LFw5O1N7YtWsXUl8N7Xd2Zuxn2Wxe9jbZVdlIBMk5J4TfeustZsyY4cg0rK/Dhgylr3tzm39ZiIqKIikp6Uqb0azc9n//R3mrDNw7qhG8ILLci+wDq09aZ/6W+SzPX37a7SullfTwSeWe6hiCKkJIjKihoU0a6imTL4f5Li4BNzc3KisrkUqluCXFk2+PJkO20THx/4/OUdc6rp+sS6S4uJjY2FhWrlx5ztlSF81Pu3btnNfhtttu44knniAuLg5w1MAeOHDAua6zF/slcO+997oc/yvE+PHj6dGjB+BoR1RUVERjYyPu7u7o9XoMhtPX3a1bt86ZHXCh6PV6vL29jy84FvF3Of4tBi8vLzp16sSUKVMoaDThrtewzLyTtcVrz7mtyWQ6Sfl8U95KMr/fSOqeeJSXMeLv4iLx8sZd50GPQimiCD4mgZXCUMx1rSkTz97/eu/evXzzzTeYTCbqzXWoGxWo/K4Np+/fgCAIZGVlsXz5cn7auBHfmgA6VEjIWfMNpblb6XnQxoGzpPvbbDZEUXR2Mmmor0JqlSMcE/l0cdUjyN2IGJnGoDlDETwPYa1IYVdVtvP/yw4vo1NwJ8oNpy/98i/cQvQdD+H11NO03tWd2BgTCQkWVCrXu/9qp3fv3lx//fUIgkD76yNYfMcqevczY7B5Yy4pvNLmXVZcjv8lIooiXbp0YfPmzcdVnl1cMWQymbPVpI+PDzfeeKNTbbhNmzYcOnTIue6zzz7L2rXnHuyfiaqqKrRaLUuXLnU5/lcBw4cP55FHHqFr166MGzeOefPmUVBQcMp6jY2NF62+npOTc5KImth4dHLB5fi3KO6++27c3NzQqVS46zz4SbKf+AqwW61kVWZhs9tOu93GjRvp3Lmz83PJup9ptXILJhQux78l4OVNdH4bZHl9mK9+BS2+bOw2m0/qH0crGhAbz1yre/jwYbp3705xcTHaRi0qoxo0rt/8lkJERATvvvsuU6dOxb/fAESpFKkoYGs0wm+/0u2D5azdcOZyj+3btzsFPf8o/IOXWU30gfbg6X3GbVxcfUyZoiM+XoYkrJr9plTa52j579//5a8jf7H34HqGqNIw2U4vVCsxlBGsd4wdDtnaEtPdn2HDrk5NAxcnk5KSQnJyMlFRUfj6HuTbxRq6p9UhqQ+htOLqaj/Z3Lgc/4vkq6++Qqt1pAYmJydz0003XWGLXJyO4cOHExwcDDjqYqurqzGZTHz99dekp6dfkijc9u3b+c9//sPWrVuvaE95Fw46duxIfHw8mZmZhIaGMmfOnJNS+j/77DMWLlxIq1atLjrTIycn5yQ1dYvJgNQmdTn+LRSd2h13vQavBjOtft9A5Q+f8En2h3yT8/Vp19+2bRsZGRkAFDUUYT+wD4BGUYWiOPey2e3iIvH2xjdCzbeeDyO54SYebvcqtz/uTwfvPIfI0wkq7/tr9p+0aX19PePGjaNr167UWupRGtXgqbncR+DiIunQoQNxcXG4ubnR6fY7+Ds+lYWhzyO1SpEbzQQaJFQf3n3G7devX0/37t0ByK7M5vGiWPxq/MEV8GlRSI82XxGCldQrgxmabWLWG9lod6zngVlLEO8ad0p3gy1btlC8by9ym43DsiSevuEIBV3uQjluFL17m/D2dk36thSSkpIoLt5B69Y2NFF++FQFkVvncvxdnAfr16/ns88+Q6lUIpPJGDNmzJU2ycV5MHnyZKZPn46HhweDBw/GYrn43ud79uwhOTmZ119/HYmr0POq4IEHHnCKnsnlcqRSKVarlfr6esrKyoiKimLIkCEolUqMRuMF77+oqIjQ0FDnZ6NZj8wq/9eL+7VUfOPa4VPvyYRtCtrWSNj/x+e0+mYZh1d8id6iP2X9Wlst3+d9z/zN81m2+WMe2uh47hsl7qhGDL3c5ru4QASJBL/pdxN/dyZjxlk4WBxLWJiFYL/Gk9q7WewW5vw955Tt1Wo1o0aNotba4HD8XRH/FkO7du2YOnUqACqVivTMnwiK9URTlECHCsdzLBw5fcqvKIro9DpndyCraEVef7Q0xPMa6ef3LyMlNRWTlyc2UYJs125ufOpzlI1WKDoCxUXO9fR6PYsXL+aD2U/RKCpYKJnKE3OMPDBHieASWG1xREdHs2bNGp55pghCWuFXHcgB88WVfrZUXN7KRWC32/H39ycvL4/o6OgrbY6LCyA0NJS33nqLoUMdg3QvLy9qa2svaB91dXX8/fffWCwW3NzcnBFAF1cfnTp1Yt26dXzxxReMGTOGXr16ERAQQJs2bU7p6X6+nFgmYDQbkFnkoHI5/i2RlM6dCbPWEFYShn+VH0uVebQvg05rDrGvfNdJ65rNZvaq99K5WMrMr0u5Z9oi3C0C+/o8jHnSDFT3T7xCR+HiQujd28Sdd+pp3drG00/vZd26dYSEWGkQPRHLy7CLdnK1uVQaK0/KDDrxb62odzn+LZAT393R0VHEZeqwHh5E8uEglpuHIa3RYi05csp2m195npzGj/hq+XysditSkwWOHEFEAC/XPdASSUtLwxRnYk+v6dTbPcFup87uhVWUIhw4rvXw6aefMmXKFEYP6EmjOYCeMXm4uUFMjPUKWu/iYpHJZEybNo2FC+dCaChuZgV6vfaS9b5aEi7H/yI4dOgQcXFxTJ482eX0tXC6devGf//7X77++vSpvadj7dq1bNy40VlC4OLqpXPnzrz00ksEBQWdFKmPiYnh0KFD52z7909OHDiabCaMVqMr4t+CadOmDRL/RpZbbmB+5busjLKRXiIlstxM/o4VJ627b98+gjw9iZgxB+F3h+qzRZQxacNMKrQKTtD8c3EV4+EhcjRwS79+XVm/fj0hYdAgani/dDFf7v+S3X8uouf6Esp3rQccuiDHusOIokid2IjCpASNx5U6DBeXSFpaGvvEBnSihl/Mw1nrPpLQBoHiDb+esu66/V9x35+t8Fi1jje2vUq7hT9DSTG4u0NrV/CnJaLRaFBEHeHlhseY5LcOsyjndcnTbLZ2g7xD2I/qfej1ekJCQjCIFairImjVxhXlb+mEh4cTEBCAReMJCjcwmaC66kqbddlwOf4XwbZt28jMzCQuLs6p8OqiZZKUlMTLL79MXl7eec/47d+/nylTpnDHHXc0s3UuLhU3NzeWLl3KjTfeeNLyqKgoFi5cyOOPP37e172urg6NRkODuQGAZzY+w0Z1BXKLHJSqJrfdRfMjCAK7O0fyU/Rs0oMO0zNPxbNVH+Jdp+HIvr9PWnfbtm2E2G1gtUKHZIQFn7F15q88MMPGr7+qrtre1S7OjEQiQSKREBCpxt7oj/SvlRR8/CIFWSsZsM9CztrvASgoKCAyMtKxkdGASZShkZsR5K7ZnpZKdHQ0+8rKENLTKUwcgU98CDFaCQcPbTxpvdqyEvTSev6v+FOG/HKQqs1/kZpVCZFRCDfdjKBWX6EjcHGpqFQGZsxo4JH/qflryHuYeg4iS9Mf3wYb2oNZzvVEUWSJbiPuBamEx7s6eVwLtG3bloOHDuEXIGCyu2M5dDzL4/eC36+gZc2Py/G/CAoLC519nF20fCQSCfHx8ezefWZhnxOx2+1IjynEuLjqOZ2Cv0Kh4Ntvv6Vv377nnfJfUFCAX4Qfty67FbtoRyFVsNSvApnFDZSKpjbbxWWiY9cg7nlgP73TKon99UFs7l5sM/XEWnRyR4iq6ircysuotAfyinQe3+T1YlNVAjfeaOCGGy5cL8LF1UFMTAxVgkjCzk7clSVDVVWLvqaUuGoJByr3Ag5F/zZt2jg2qG/AhAIv9emVv120DCQSCaIo0nZ0KoGD0/Bp441vtT8HKx2CndXGaoxWI5/+8hx99vpTZg+h2ubH3HcPEmSQYH5wJm4+royPlk5ysoX0TnYWHbmB/jep0GlCCdILlB3Owm63I5FI+P7g9ww7rMBiCkAT68r0vBZo3749e/bsIaK1iHtNCPkHNwMg2u08v+opKqqv3RZ/Lsf/InjooYcuuh2Yi6uTvn37snz58nOuZzAYnAI/Llo2EomEvn37snLlyvNa//Dhw+yS7+KuhLv4dO+nJPglkKB1c6T6uyL+LZbevTtTUbGcxLvS+NZ2F3OfN5AlZoJBj6jXOdczCgb8D5awzDyCMfe5IZVCcbEUpRJmzz57D3gXVy8ZGRnsqaxCbnFDEAV6FMiwScC3UUBbVwJAbm4uMTEx2Ow2vjrwFTpBgcb99C0fXbQclEolvXvXcPvtepIHeHHYkEF9fTm/5i7lg61vMHfdHEoKs6C8I7e1W8kWsZtjw8Qk1suHEBHhugdaMp6entTV1SEIcNttBnr0MCF6+xCgF6gozqGiooKAgAAOaA+QvvfoOz484soa7aJJiIqKoqCggNYJCjyOJPFL5RoAtEs+J3V7GWsXPXWFLWw+XI7/ReBy/K49PD09qa6uxmo9u2DL9u3bSUlJuUxWuWhuAgICOHToEPfffz/5+flnXTe/IJ9A30BGxozkk72f0Ce8DxN3aQiqCHLV+LdgAgICqKqqQpKRwecbvPEb1hWrp6/jnwWOqH+lrhKpsYjIEj2VqjaEdI7g5puNzJnjcvhbOuHh4RzU6xEQ+d48huzCe3loiyOF36ZvQKyro7GxEZVKxV8Ff2Cvq8Wr3gtPjcvpa+n07duXNWt+R6WCpAw5u736kK+xYt60jpmP/sicV7J4ZHkt+20J3DSnLXtvf51PRm/ipYSlVFZKGTHClenTkjlR5Hfo0EbkcghrI4WGVhTWHGTJniXIg+RElBodHT9kUggOucJWu2gKjmX8hKX6oatLJKq0kb+O/MWOXb9y8z4ZB0qzr7SJzYbL8Xfh4iijRo3ihx9+OOs627ZtIy0t7TJZ5OJyMH78eJ588klWrFhx1vUsZgsPpD6AVCLl3ZR5eI+4GY8jBrxNuFL9WzgymQyLxUJIiKN/c6tgC1aTF7r8/dSaarl56c2o7BVE1UoQIsKdGV+env8eJeBrFUEQqPX0QuzZh/19ZlAsicHXIGGHNZ3UMgm/bfkUERFRFNn402uMnvU5nbMS8PS0n3vnLq5qEhIS2LNnDwAqlUiDd2teXaHg+hd+AL0eed5hfPVmtAHxBHaP5XCRirCMYGY+aWb0aJfT39KJjo7m0KFDJy1L6SrlSF1n/uQgBZUFLCp/n8EvLXH8MzUdwVXmec0gkUiwtgrAKsq54Zc81uQuJ1u7h6RKCWi12Kurr7SJzUKzOP47d+5k6tSpPPTQQyxZsqQ5vsKFiyYnNTWVnJycsyq9G41GV8bHNUZcXBytWrWiqurcqq6itgbxt1+J/eYPKC7CJCpRCo2uVP8WTkpKCjt37nR+jo01I9NGUHgkmx8P/UhvSW+WafYRVC9DGhF+xex00TwkJSVhiHSnx+gAOvbzZIbkCz7x/i8DDsvIKdhKtrCSeb88TMzGAwgI1IteeHm7yv1aOoIg4OPjQ/XRAX5ydyXZlnQAjOHtsIlHh8hJHQB44YU6Bg50aTtcK4SHh7N161bWrFnjXBbXK4DD5kQ++dLCoFVVLFgs4lNrwnDdLai7u4I+1xK33347b//4E8gdnRqun/c9GzxrUFoE7sqSIe7YcoUtbB6a3PG32+189NFHzJo1i1deeYX169dTVFTU1F/jwkWzMHXqVF588UUMBsMp/9PpdLi7uxRdr1V8fX2dA8B/IooisYcPIQ4fjPjIVPjyMwAaRSX/3969B0V1pmkAf/oCQnNpoLk4QFBAvKBxHIURoxFREkeT1GRMZFcnF4qkphQTSl2dwNasujFUrFICScBBsynIsEmmaszqhJ2UTmEVGFAyCmiURAIEkQlqSzeXvnDrPt/+QYUNiUaYAZtzeH7/ddcHvF1PnY/z9jnfdzzQC0zjFX85W7p0Kd5//32UlpbCbrcjcoEn3G4sxB8tZ9DS/Dds/GMtVjQNoE2ah1krQ1xdLo2zRx99FFrtUSQl9WNtXjKeK0rAg0tUMEsGpL/zOd77w9fIyvwE/3Jl6JSpR+jh68e7PZRg48aNePPNN9HY2IhGXRk+WlOMwT98hL3zyvGnJb/HxfD50MYMPbLP25uZK4mbmxsee+wxNDc3o7KyEgCgNfjDiaGr+g9XVSCo6Rtg1my0P/+fCA/n8h4lCQ4OxvyFC9E+JxZYuAg/u6XBnk/dkWo9Bp3NF6qaWleXOCE0+/bt2zeev7CxsRHXr1/HunXroFarYbPZ0N7ejnnz5v3oz1kslvEsY8LpdLo7NockXzqdDk6nEwsXLkR+fj68vLxQUlKCuro6xMbG4vz584iOjh7xPHia/EZ7rEZERKCgoADh4eEoLi6Gp6cnrly5Ar1eD2mgHz95Kweend+5GyR2AW7bfWHym4PYtJ9P4CegOxnPOdjd3R2LFi2Cu7s7PvzwQ3S11qOzbh62Nf0vIuuuYe7fO7Dquhaf/iQND/4mHgEBbAAmiiv+t6rVarS2XsOpU6dw7lwl5szxgtHZB/PNEMzpqMD3r+2fGVyN5T5/g/apDfe1TjmbrOdMOp0OM2fOxOnTp/HU07/CXys+wsmaZGRkSDjdOhf/070QWf/uBy8vHvN3MllzHa0ZM2Zg0aJF+OCDD1BVVYW6ujpI1yMQ11uGbr0PdL9JR83abHz4cTCSkvoRFDQ1lvjIPdfRiomJwfHyTlwJ7cWKhhpYLbNh9JmDv9tD8FPxGVQb/9XVJY6aj4/PqMapxGgfYj1K1dXVuHjxIrZs2QIAOHPmDBobG/HCCy+MGFdWVoaysjIAwIEDBzAwMDCeZUw4rVZ7z43gSF6+m+lnn32Gq1ev4rnnnoPRaMTRo0dhs9nw6quvwt2dz26Wk7Ecqw0NDfjkk0+QmpqK8vJyTJ8+HVVVVejp6cHGeXMxa3AA7mt/gb73S3B7+a9hGtTjevs0/CpFO8Gfgr5vIufg7qYmZC/5GLt0r6FPTINl9kwE2+3Y/8DHyD02A1zmOXFc/b/VZDKhoqICvr7+OLBfhX/T7MGMlCy4X/sSbS0OnGxbAtRfxL53wuCZIp+TQldzda6jJUkSCgoK0NXVhfZ2f0RFrcfu3VGuLmvSkkuuo9XS0oKDuz7FTMsXcCxfjE7rJixbJuGJJwTc3Fxd3f2jtFx/zF/+okJQENS7o/cAAAnOSURBVBB45R3k/4cVYU+040LZz/Ffb+ngtX69q8sbtdH2JuPe+J87dw6XLl0a0fg3NTUhLS3tR3+uvb19PMuYcIGBgaNaE0zywUyVaSJyFQLIyPCDj49AcnIfVq/mus/7bSKPVyEEDi74E54SRXjF/wT++/Q0HDumw9y5g4iLG5yQv0lDJtM8nJvrDUlSwekEnM6h416tElB33sbu19250dcYTKZcafwoMddbt9TYscMPycn9ePZZ25Rq+L+lxFzvprtbhaNHvSEE4OUlsG2bFSaTGv7+EtQy2gI/NDR0VOPG/TKVwWAYsU7WZDLB399/vP8MEdF9JUlAYaE3urpUmDHDiV/+shfHjung4cFbQJVGpVJBtW49/qpeib3PeuO3v/XCunV9bPqnmB07rLBaVSPWdv/5zx4oLQ2FStPpwsqIaKKEhEg4erSTezpMEXq9wO7dI5ebGwzKXdIx7t9lREdH48aNGzAajXA4HDh79izi4uLG+88QEd1XajXw/PM27NxpgVoNrFnTj9/9rgdz5kyN2+GmmtCfBaNhYC4efHAQb73VhXXr+lxdErnA90/+ExP7YTLJ6DIQEY0Zm35SqnG/4q/RaJCWlobs7GxIkoSkpCQ88AAff0RE8vftBk+bNg1tesNdfpUrMtIBq5WPbKOR/PwEtmyxuboMIiKiMZuQHakWL16MxYsXT8SvJiIimnAJCQOIi5PXprN0f6xdy7s/iIhIfni/GhER0feo1QAf4EFERERKwcafiIiIiIiISMHY+BMREREREREpGBt/IiIiIiIiIgVj409ERERERESkYGz8iYiIiIiIiBSMjT8RERERERGRgrHxJyIiIiIiIlIwlRBCuLoIIiIiIiIiIpoYvOL/D8rMzHR1CTTOmKkyMVdlYq7KxFyVibkqE3NVJuaqXGz8iYiIiIiIiBSMjT8RERERERGRgmn27du3z9VFyFVUVJSrS6BxxkyVibkqE3NVJuaqTMxVmZirMjFXZeLmfkREREREREQKxlv9iYiIiIiIiBSMjT8RERERERGRgmldXYDcXLx4EUVFRZAkCWvWrMGTTz7p6pJolA4fPoza2lro9Xrk5OQAAKxWK3Jzc3H79m0EBQVhx44d8Pb2hhACRUVFqKurw7Rp05Cens71TpNUR0cHCgoK0NXVBZVKheTkZKxfv57ZytzAwAD27t0Lh8MBp9OJhIQEpKSkwGg0Ii8vD1arFZGRkXj55Zeh1WoxODiI/Px8fP311/Dx8cH27dsRHBzs6o9BdyBJEjIzMxEQEIDMzExmqgDbtm2Dh4cH1Go1NBoNDhw4wDlYAWw2GwoLC9HW1gaVSoWtW7ciNDSUucpYe3s7cnNzh18bjUakpKQgMTGRuU4FgkbN6XSKl156Sdy8eVMMDg6KXbt2iba2NleXRaNUX18vmpubxc6dO4ffKykpEcePHxdCCHH8+HFRUlIihBCipqZGZGdnC0mSRENDg8jKynJJzXRvZrNZNDc3CyGEsNvtIiMjQ7S1tTFbmZMkSfT29gohhBgcHBRZWVmioaFB5OTkiMrKSiGEEEeOHBGnTp0SQghx8uRJceTIESGEEJWVleKNN95wTeF0T6WlpSIvL0+8/vrrQgjBTBUgPT1ddHd3j3iPc7D8vf3226KsrEwIMTQPW61W5qogTqdTvPjii8JoNDLXKYK3+o9BU1MTpk+fjpCQEGi1Wjz00EM4f/68q8uiUYqNjYW3t/eI986fP4/ExEQAQGJi4nCeFy5cwMqVK6FSqTB79mzYbDZ0dnbe95rp3vz9/Ye/ffb09ERYWBjMZjOzlTmVSgUPDw8AgNPphNPphEqlQn19PRISEgAAq1atGpHrqlWrAAAJCQm4cuUKBPeunXRMJhNqa2uxZs0aAIAQgpkqFOdgebPb7fjyyy+xevVqAIBWq4WXlxdzVZDLly9j+vTpCAoKYq5TBG/1HwOz2QyDwTD82mAwoLGx0YUV0T+ru7sb/v7+AIYayJ6eHgBDWQcGBg6PMxgMMJvNw2NpcjIajWhpacGsWbOYrQJIkoRXXnkFN2/exNq1axESEgKdTgeNRgMACAgIgNlsBjByftZoNNDpdLBYLPD19XVZ/fRDxcXFeOaZZ9Db2wsAsFgszFQhsrOzAQCPPPIIkpOTOQfLnNFohK+vLw4fPozW1lZERUUhNTWVuSpIVVUVli9fDoDnw1MFG/8xuNOVBpVK5YJKaKIxa/np6+tDTk4OUlNTodPp7jqO2cqHWq3GwYMHYbPZcOjQIXzzzTd3HctcJ7+amhro9XpERUWhvr7+nuOZqXzs378fAQEB6O7uxmuvvYbQ0NC7jmWu8uB0OtHS0oK0tDTExMSgqKgIJ06cuOt45iovDocDNTU12Lx584+OY67KwsZ/DAwGA0wm0/Brk8nEb7xkTq/Xo7OzE/7+/ujs7By+kmQwGNDR0TE8jllPbg6HAzk5OXj44YexdOlSAMxWSby8vBAbG4vGxkbY7XY4nU5oNBqYzWYEBAQA+P/52WAwwOl0wm63/2BpD7lWQ0MDLly4gLq6OgwMDKC3txfFxcXMVAG+zUyv1yM+Ph5NTU2cg2XOYDDAYDAgJiYGwNBymxMnTjBXhairq0NkZCT8/PwA8JxpquAa/zGIjo7GjRs3YDQa4XA4cPbsWcTFxbm6LPonxMXFoaKiAgBQUVGB+Pj44ffPnDkDIQS++uor6HQ6TnSTlBAChYWFCAsLw+OPPz78PrOVt56eHthsNgBDO/xfvnwZYWFhmD9/PqqrqwEA5eXlw3PwkiVLUF5eDgCorq7G/PnzeVViktm8eTMKCwtRUFCA7du3Y8GCBcjIyGCmMtfX1ze8dKOvrw+ff/45IiIiOAfLnJ+fHwwGA9rb2wEMrQcPDw9nrgrx3dv8AZ4zTRUqwZ1yxqS2thbvvfceJElCUlISNmzY4OqSaJTy8vLwxRdfwGKxQK/XIyUlBfHx8cjNzUVHRwcCAwOxc+fO4ceXvPvuu7h06RLc3d2Rnp6O6OhoV38EuoOrV69iz549iIiIGG4KNm3ahJiYGGYrY62trSgoKIAkSRBCYNmyZXj66adx69atHzz6zc3NDQMDA8jPz0dLSwu8vb2xfft2hISEuPpj0F3U19ejtLQUmZmZzFTmbt26hUOHDgEYuj18xYoV2LBhAywWC+dgmbt27RoKCwvhcDgQHByM9PR0CCGYq8z19/dj69atyM/PH14ayeN1amDjT0RERERERKRgvNWfiIiIiIiISMHY+BMREREREREpGBt/IiIiIiIiIgVj409ERERERESkYGz8iYiIiIiIiBSMjT8RERERERGRgrHxJyIiIiIiIlKw/wOE3SxqPonT6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat_hat10 = np.percentile(result, 10, axis = 2)\n",
    "mat_hat90 = np.percentile(result, 90, axis = 2)\n",
    "mat_hat = np.mean(result, axis = 2)\n",
    "\n",
    "X = dense_mat.copy()\n",
    "pred_steps = int(num_roll * num_step)\n",
    "tv = 108\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "figsize = 2\n",
    "for i in range(3):\n",
    "    fig = plt.figure(figsize = (8 * figsize, 2 * figsize))\n",
    "    ax = fig.add_axes([0.13, 0.28, 0.85, 0.68])\n",
    "    plt.plot(X[i, 18 * tv :], color = \"black\", linewidth = 0.5)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 18 * tv, X.shape[1] - 18 * tv)), \n",
    "             mat_hat[i, :], color = \"#e3120b\", linewidth = 2.0)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 18 * tv, X.shape[1] - 18 * tv)), \n",
    "             mat_hat10[i, :], color = \"blue\", linewidth = 0.5)\n",
    "    plt.plot(list(range(X.shape[1] - pred_steps - 18 * tv, X.shape[1] - 18 * tv)), \n",
    "             mat_hat90[i, :], color = \"green\", linewidth = 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "\n",
    "tensor = scipy.io.loadmat('../datasets/Hangzhou-data-set/tensor.mat')\n",
    "tensor = tensor['tensor']\n",
    "random_matrix = scipy.io.loadmat('../datasets/Hangzhou-data-set/random_matrix.mat')\n",
    "random_matrix = random_matrix['random_matrix']\n",
    "random_tensor = scipy.io.loadmat('../datasets/Hangzhou-data-set/random_tensor.mat')\n",
    "random_tensor = random_tensor['random_tensor']\n",
    "\n",
    "dense_mat = tensor.reshape([tensor.shape[0], tensor.shape[1] * tensor.shape[2]])\n",
    "missing_rate = 0.0\n",
    "\n",
    "# =============================================================================\n",
    "### Random missing (RM) scenario\n",
    "### Set the RM scenario by:\n",
    "binary_mat = np.round(random_tensor + 0.5 - missing_rate).reshape([random_tensor.shape[0], \n",
    "                                                                   random_tensor.shape[1] \n",
    "                                                                   * random_tensor.shape[2]])\n",
    "# =============================================================================\n",
    "\n",
    "sparse_mat = np.multiply(dense_mat, binary_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/xinyuchen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:18: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: nan\n",
      "\n",
      "2160\n",
      "2165\n",
      "2170\n",
      "2175\n",
      "2180\n",
      "2185\n",
      "2190\n",
      "2195\n",
      "2200\n",
      "2205\n",
      "2210\n",
      "2215\n",
      "2220\n",
      "2225\n",
      "2230\n",
      "2235\n",
      "2240\n",
      "2245\n",
      "2250\n",
      "2255\n",
      "2260\n",
      "2265\n",
      "2270\n",
      "2275\n",
      "2280\n",
      "2285\n",
      "2290\n",
      "2295\n",
      "2300\n",
      "2305\n",
      "2310\n",
      "2315\n",
      "2320\n",
      "2325\n",
      "2330\n",
      "2335\n",
      "2340\n",
      "2345\n",
      "2350\n",
      "2355\n",
      "2360\n",
      "2365\n",
      "2370\n",
      "2375\n",
      "2380\n",
      "2385\n",
      "2390\n",
      "2395\n",
      "2400\n",
      "2405\n",
      "2410\n",
      "2415\n",
      "2420\n",
      "2425\n",
      "2430\n",
      "2435\n",
      "2440\n",
      "2445\n",
      "2450\n",
      "2455\n",
      "2460\n",
      "2465\n",
      "2470\n",
      "2475\n",
      "2480\n",
      "2485\n",
      "2490\n",
      "2495\n",
      "2500\n",
      "2505\n",
      "2510\n",
      "2515\n",
      "2520\n",
      "2525\n",
      "2530\n",
      "2535\n",
      "2540\n",
      "2545\n",
      "2550\n",
      "2555\n",
      "2560\n",
      "2565\n",
      "2570\n",
      "2575\n",
      "2580\n",
      "2585\n",
      "2590\n",
      "2595\n",
      "2600\n",
      "2605\n",
      "2610\n",
      "2615\n",
      "2620\n",
      "2625\n",
      "2630\n",
      "2635\n",
      "2640\n",
      "2645\n",
      "2650\n",
      "2655\n",
      "2660\n",
      "2665\n",
      "2670\n",
      "2675\n",
      "2680\n",
      "2685\n",
      "2690\n",
      "2695\n",
      "Final MAPE: 0.582281\n",
      "Final RMSE: 75.4304\n",
      "\n",
      "Running time: 866 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 108])\n",
    "num_step = 5\n",
    "num_roll = int(108 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 100\n",
    "gibbs_iter = 10\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/xinyuchen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:18: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 2\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 3\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 4\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 5\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 6\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 7\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 8\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 9\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 10\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 11\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 12\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 13\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 14\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 15\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 16\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 17\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 18\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 19\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 20\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 21\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 22\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 23\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 24\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 25\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 26\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 27\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 28\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 29\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 30\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 31\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 32\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 33\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 34\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 35\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 36\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 37\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 38\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 39\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 40\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 41\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 42\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 43\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 44\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 45\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 46\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 47\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 48\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 49\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 50\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 51\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 52\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 53\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 54\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 55\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 56\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 57\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 58\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 59\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 60\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 61\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 62\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 63\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 64\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 65\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 66\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 67\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 68\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 69\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 70\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 71\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 72\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 73\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 74\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 75\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 76\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 77\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 78\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 79\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 80\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 81\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 82\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 83\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 84\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 85\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 86\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 87\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 88\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 89\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 90\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 91\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 92\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 93\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 94\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 95\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 96\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 97\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 98\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 99\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 100\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 101\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 102\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 103\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 104\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 105\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 106\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 107\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 108\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 109\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 110\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 111\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 112\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 113\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 114\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 115\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 116\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 117\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 118\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 119\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 120\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 121\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 122\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 123\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 124\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 125\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 126\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 127\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 128\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 129\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 130\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 131\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 132\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 133\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 134\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 135\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 136\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 137\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 138\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 139\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 140\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 141\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 142\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 143\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 144\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 145\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 146\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 147\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 148\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 149\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 150\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 151\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 152\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 153\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 154\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 155\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 156\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 157\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 158\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 159\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 160\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 161\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 162\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 163\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 164\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 165\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 166\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 167\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 168\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 169\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 170\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 171\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 172\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 173\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 174\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 175\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 176\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 177\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 178\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 179\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 180\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 181\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 182\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 183\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 184\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 185\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 186\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 187\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 188\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 189\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 190\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 191\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 192\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 193\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 194\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 195\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 196\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 197\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 198\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 199\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 200\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 201\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 202\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 203\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 204\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 205\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 206\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 207\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 208\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 209\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 210\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 211\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 212\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 213\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 214\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 215\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 216\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 217\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 218\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 219\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 220\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 221\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 222\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 223\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 224\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 225\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 226\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 227\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 228\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 229\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 230\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 231\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 232\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 233\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 234\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 235\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 236\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 237\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 238\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 239\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 240\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 241\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 242\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 243\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 244\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 245\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 246\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 247\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 248\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 249\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 250\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 251\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 252\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 253\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 254\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 255\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 256\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 257\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 258\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 259\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 260\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 261\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 262\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 263\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 264\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 265\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 266\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 267\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 268\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 269\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 270\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 271\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 272\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 273\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 274\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 275\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 276\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 277\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 278\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 279\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 280\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 281\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 282\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 283\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 284\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 285\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 286\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 287\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 288\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 289\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 290\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 291\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 292\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 293\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 294\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 295\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 296\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 297\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 298\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 299\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 300\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 301\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 302\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 303\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 304\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 305\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 306\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 307\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 308\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 309\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 310\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 311\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 312\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 313\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 314\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 315\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 316\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 317\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 318\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 319\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 320\n",
      "RMSE: nan\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 321\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 322\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 323\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 324\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 325\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 326\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 327\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 328\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 329\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 330\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 331\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 332\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 333\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 334\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 335\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 336\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 337\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 338\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 339\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 340\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 341\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 342\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 343\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 344\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 345\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 346\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 347\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 348\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 349\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 350\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 351\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 352\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 353\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 354\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 355\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 356\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 357\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 358\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 359\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 360\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 361\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 362\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 363\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 364\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 365\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 366\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 367\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 368\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 369\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 370\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 371\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 372\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 373\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 374\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 375\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 376\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 377\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 378\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 379\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 380\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 381\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 382\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 383\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 384\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 385\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 386\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 387\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 388\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 389\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 390\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 391\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 392\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 393\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 394\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 395\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 396\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 397\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 398\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 399\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 400\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 401\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 402\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 403\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 404\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 405\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 406\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 407\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 408\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 409\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 410\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 411\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 412\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 413\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 414\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 415\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 416\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 417\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 418\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 419\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 420\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 421\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 422\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 423\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 424\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 425\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 426\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 427\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 428\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 429\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 430\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 431\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 432\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 433\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 434\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 435\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 436\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 437\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 438\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 439\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 440\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 441\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 442\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 443\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 444\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 445\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 446\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 447\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 448\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 449\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 450\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 451\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 452\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 453\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 454\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 455\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 456\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 457\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 458\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 459\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 460\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 461\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 462\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 463\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 464\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 465\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 466\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 467\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 468\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 469\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 470\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 471\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 472\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 473\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 474\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 475\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 476\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 477\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 478\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 479\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 480\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 481\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 482\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 483\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 484\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 485\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 486\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 487\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 488\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 489\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 490\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 491\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 492\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 493\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 494\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 495\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 496\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 497\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 498\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 499\n",
      "RMSE: nan\n",
      "\n",
      "Iteration: 500\n",
      "RMSE: nan\n",
      "\n",
      "2160\n",
      "2165\n",
      "2170\n",
      "2175\n",
      "2180\n",
      "2185\n",
      "2190\n",
      "2195\n",
      "2200\n",
      "2205\n",
      "2210\n",
      "2215\n",
      "2220\n",
      "2225\n",
      "2230\n",
      "2235\n",
      "2240\n",
      "2245\n",
      "2250\n",
      "2255\n",
      "2260\n",
      "2265\n",
      "2270\n",
      "2275\n",
      "2280\n",
      "2285\n",
      "2290\n",
      "2295\n",
      "2300\n",
      "2305\n",
      "2310\n",
      "2315\n",
      "2320\n",
      "2325\n",
      "2330\n",
      "2335\n",
      "2340\n",
      "2345\n",
      "2350\n",
      "2355\n",
      "2360\n",
      "2365\n",
      "2370\n",
      "2375\n",
      "2380\n",
      "2385\n",
      "2390\n",
      "2395\n",
      "2400\n",
      "2405\n",
      "2410\n",
      "2415\n",
      "2420\n",
      "2425\n",
      "2430\n",
      "2435\n",
      "2440\n",
      "2445\n",
      "2450\n",
      "2455\n",
      "2460\n",
      "2465\n",
      "2470\n",
      "2475\n",
      "2480\n",
      "2485\n",
      "2490\n",
      "2495\n",
      "2500\n",
      "2505\n",
      "2510\n",
      "2515\n",
      "2520\n",
      "2525\n",
      "2530\n",
      "2535\n",
      "2540\n",
      "2545\n",
      "2550\n",
      "2555\n",
      "2560\n",
      "2565\n",
      "2570\n",
      "2575\n",
      "2580\n",
      "2585\n",
      "2590\n",
      "2595\n",
      "2600\n",
      "2605\n",
      "2610\n",
      "2615\n",
      "2620\n",
      "2625\n",
      "2630\n",
      "2635\n",
      "2640\n",
      "2645\n",
      "2650\n",
      "2655\n",
      "2660\n",
      "2665\n",
      "2670\n",
      "2675\n",
      "2680\n",
      "2685\n",
      "2690\n",
      "2695\n",
      "Final MAPE: 0.514535\n",
      "Final RMSE: 74.9771\n",
      "\n",
      "Running time: 4369 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "start = time.time()\n",
    "dim1, dim2 = sparse_mat.shape\n",
    "rank = 10\n",
    "time_lags = np.array([1, 2, 108])\n",
    "num_step = 5\n",
    "num_roll = int(108 * 5 / num_step)\n",
    "start_time = dim2 - num_roll * num_step\n",
    "init = {\"W\": 0.1 * np.random.rand(dim1, rank), \n",
    "        \"X\": 0.1 * np.random.rand(start_time, rank)}\n",
    "burn_iter = 500\n",
    "gibbs_iter = 50\n",
    "result = forecastor(dense_mat, sparse_mat, init, time_lags,\n",
    "                    num_roll, start_time, num_step, burn_iter, gibbs_iter)\n",
    "end = time.time()\n",
    "print('Running time: %d seconds'%(end - start))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
